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How to Write an Artist’s CV in 10 Steps.
A CV or curriculum vitae is an *richtlijnen thesis vub* overview of your artistic professional history and achievements. Although it looks similar to a resume, it contains different elements which are only **amusement park** related to your artistic professional practice.
One mistake emerging artists often make in writing their CVs is trying to **richtlijnen** oversell their work. *Gpa On Resume*. Less is more. Your CV should be neatly organized, and **richtlijnen thesis** only include information pertinent to **nora ephron essay about** your artistic career.
What should you include on vub a CV? Here is where how to compose one in 10 steps:

Often, more established artists will keep it simple. *A Few About Breasts*. This is **thesis** because their CV is **nora ephron essay a few words about** usually referenced as a biography rather than a resume.
Damian Hirst (b. 1965, UK)
However, you can include contact information if you are sending out your CV to **richtlijnen thesis vub** galleries in *resume*, the hopes that they will reply:
Damian Hirst, (b.

1965, UK)
Either of these formats is appropriate for **richtlijnen thesis**, an artist’s CV. Just keep in mind that you should only include your website if it directly relates to **nora ephron** your artistic practice.
You may have attended post-secondary school for art, or you might be a self-taught, mentored, or otherwise educated artist. Generally speaking, this section of a CV relates to institutional education specifically in the field of visual arts.

If you do have post-secondary education in the arts field, include the school(s), the year(s) that you graduated, and the degree(s):
University of British Columbia, Master of Fine Arts, 2009.
Emily Carr University, Bachelor of Fine Arts, 2005.
If you do not have a degree in the visual arts field, fear not. This section of the CV is **richtlijnen thesis** not a pre-requisite for exhibitions or gallery representation. The only thing to note is that you should not put down any other type of education (high school graduation, degree in business management), unless it very directly relates to the artwork that you make. Leaving this section off of your CV is **paper** perfectly acceptable.
Beginning with your most recent, you should list your exhibitions in a manner similar to this:
2011 Title of richtlijnen thesis vub Show , Museum of Modern Art, NY.
2010 I’ve been showing a lot lately , Galerie Espace, Montreal.

If you have a large number of exhibitions, you can split them into two or more categories: solo exhibitions, group exhibitions, and even duo exhibitions. This helps define in what capacity your work was shown (you don’t want to **gpa on resume** undersell your solo show at the MoMA.)
A method often used by *richtlijnen thesis*, artists is to list “selected” exhibitions, ie, the heading would read “selected group exhibitions”. This has benefits whether you have a lot of exhibitions or not: if you have lots, you can weed out the exhibitions that are no longer relevant to your career. *Adding*. If you don’t have a lot of exhibitions, you are assuring the reader that they are not looking at a short list, but rather your most relevant history.
In this section of your CV, you can include any articles in which you or your art appeared.

If it is an article, it should include the author, title, publication, volume, publication date, and page number:
Coupland, Douglas: “Why I Love This Artwork”, Canadian Art Magazine, vol. 12, February 2011, p. 55-60.
If your work appeared on the cover of a publication, you can format your information like this:
Canadian Art Magazine, Cover, vol. *Richtlijnen Thesis Vub*. 12, February 2011.
If writing about your artwork or your artwork itself appears in a book, the formatting should read:
Schwabsky, Barry (Compiler), Vitamin P: New Perspectives in Painting , Phiadon Press 2004, p. 78.
For further information and other examples of MLA format, there any many resources online. *Nora Essay A Few About*. As an example, here is SFU’s citation guide for MLA style .
Once I entered a competition to paint banners for **richtlijnen thesis**, a small city’s Christmas celebration. I requested the banner be returned when the competition was over, but they refused to return it.

Now I put “City of _____” under the *park essays*, public collections section of my CV. We both win!
Generally, the “collections” portion of your CV is to list public institutions which own your artwork. This could be museums, corporate collections, or even municipalities or agencies. They can simply be listed under the heading collections:
The Vancouver Art Gallery.
The Canada Council Art Bank.
The Colart Collection.
If you only have artwork in private collections and you wish to **thesis vub** include this section on memory essays death your CV, you should not list the name of the collector unless 1. they are well-known as important collectors of richtlijnen vub art, and 2. have explicitly agreed to be listed on your CV in whatever venue it gets published (the web, etc).

If several people own your artwork in *paper on identity*, private collections and **thesis** you would like to note that, you can list them like this:
Private collection, Calgary AB.
Private collection, Vancouver, BC.
Just don’t go to overboard with the *essay club*, list– if you really have lots, you’ll look more understated and impressive by inserting something like this:
Works held in *richtlijnen vub*, private collections in Canada, the *nora ephron words breasts*, United States, Germany, and New Zealand.
If you have any published writing relating to either your own practice or that of others, you can list it here in proper MLA format:
“This Artwork is Awesome”, Awesome exhibition catalogue, Vancouver Art Gallery, 2006.
The above points are the most common and usually the most notable elements which artists include on their CVs.

However, depending on your practice, there may be a number of richtlijnen thesis other professional and artistic points of essay a few words breasts interest to **vub** list. Here are some examples:
This is a space to list any teaching positions you may have had, either as a faculty member or as a guest lecturer or speaker. You should only include those related specifically to your practice or to visual arts:
2009, Guest lecturer, Emily Carr University.
2007, Sessional instructor, SFU.
If, as well as being an artist you have also undertaken curatorial projects (as so many artists seem to do now), you can list them simply as the *nora words breasts*, exhibition itself, or, add on a brief explaination:
2011, “Drawings”, Richmond Art Gallery.

2010, “Paintings”, Or Gallery, co-curated by Damian Hirst.
Some artists choose to list awards and / or grants they have received. *Richtlijnen Thesis*. If you decide to include this, the list should all be specifically related to your artistic practice, unless it is extremely notable, such as the Nobel Peace Prize:
2011, Canada Council grant.
2010, BC Arts Council grant.
Artist’s residencies you may have attended are good to include on research paper your CV as they show a dedication to your practice and to your professional development:
2010, Studio residency, School of Visual Arts, New York.
One of the best ways to start writing your CV is to see how other artists do it. In addition to the categories listed above, there are many different professional practices or ways of organizing your information.

Many galleries or artist’s themselves post CVs on their website, so they are easily accessible. A few to check out:
143 thoughts on “ How to Write an Artist’s CV in 10 Steps ”
Thanks so much, great information.
really great,, I was struggling on puting one together,
The information online is very conflicting when it comes to artists CV’s.
thia article only applies to artists with sufficient experience and **richtlijnen thesis** various accomplishments such that this article would provide no value, with no usefulness or relevance to artists who are seeking advice on creating a resume.
Hi Bradley– I’d be happy to **law assignments** give you other suggestions for **vub**, your artist CV.

What kind of artistic experience do you have, and what were you thinking of including on your CV? What would you reccommend to write in an unexperienced artist?s cv? I don?t even have shown my work in a gallery, do you think it is a must to do this? What would be the previous steps to writing a cv? I am interested in applying for a contest but I always end up not applying because of the cv. Wow. This blog is such a fantastic resource!

I am thrilled to have found it this afternoon! Cheers!
If you are creating a resume for **memory essays theatre death**, an art teacher position, do you still include all the *richtlijnen thesis*, info you pointed out? Or do you create more of a standard resume (objective, job history, etc.)? Do they want to see if your work has been in galleries, etc?
Hi Tanya, I would still use all the info listed above, but perhaps pare it down to include only the “highlights.” Then you can also include standard employment info from a regular resume, as well as references. Cheers!

Thanks for the info. *Body Theatre Death*. Also, should I put experience first, then the highlights of CV? Also, is their a max for **thesis vub**, number of pages, because I know on my standard employment resume you shouldn’t have more than 2 pages.
Apologies for the delayed reply! I agree experience first and then CV highlights. I’d keep it to **park essays** 2 pages if possible, but if the position you are applying for is prestigious or highly competitive, they would probably appreciate more information. *Vub*. For example, the *nora ephron a few breasts*, CVs of many scholars are pages and pages long!
If you do not have a formal art degree but have taken collegiate courses, should you include the university and disciplines under Education?

I was originally enrolled in a 4 year art program and **thesis** due to a significant change in circumstances had to move and **ephron essay words breasts** was forced to complete a 2 year general degree. My CV is **richtlijnen** really short, although I’m working on getting more exhibitions under my belt.
Hi Diana, yes, I would include these collegiate courses but keep them brief. I would list the general degree and **law assignments** highlight your original focus on the arts-related courses.
What if you have no experience, have taken photography classes and have only shown in student shows? How can you put something together with practically nothing without making it look that way?
Hi Lisa, you should list your photography courses under education and your student shows under exhibitions. If anyone owns your work (even if you’ve gifted them a work,) you can list them as a private collection (see step 5.) Those three items formatted nicely with your contact info should give you a decent 1 page CV. Don’t worry if it seems sparse to you, there’s nothing wrong with being an emerging artist! Also remember most people will look at *thesis* your artwork before they look at your CV #128521;
Thank you for the information – it’s very helpful!

One other question – as far as publications is concerned: what if my art appeared in *research paper*, a [student] publication, but wasn’t reviewed? The book appears every spring and consists of photos of various students’ work. *Richtlijnen Vub*. Should I put that on a CV or leave it out?
Hi Lisa, definitely include it. Any time your artwork is published it’s worth including!
A couple of questions:
I have several exhibitions from the *memory death*, Navy, should they be listed by ship or simply U.S. Navy with home city and **richtlijnen thesis vub** year?
I also received a nomination for 2005 Graphic Artist of the Year while in the Navy, which section would you recommend listing this?
Hi Michael, for **paper**, your exhibitions, I think you should list U.S.

Navy, the ship, as well as home city and **richtlijnen vub** year. Someone looking at *research paper on identity* your CV would probably appreciate as much information as possible.
For your nomination (congratulations, by *richtlijnen vub*, the way!) you can list that under a heading called “awards.” You could format it something like this:
2005, Nomination, Graphic Artist of the Year, US Navy.
I hope that helps #128578;
Very much so.

Thank you!
OK, one more question, for multiple awards received in one year, list year and award individually or as a group under that one year?
Hi Michael, there’s no exact right or wrong here, it’s up to **essays** you in *richtlijnen thesis*, terms of what you think visually looks better. *Essays*. You could go like this:
Nominated, Award #1.
Nominated, Award #2.
Finalist, Award #3.
2005, Nominated, Award #1.
2005, Nominated, Award #2.
2005, Finalist, Award #3.

2004, Winner, Award #4.
just saying thank you. i have struggled to **thesis** find a good reference for creating a cv for **research paper**, an artist, this one is great.
Thank you! I’m glad it helped you.
I was wondering whether the tips above applies to those wanting to pursue arts-management courses as well? . I don’t have formal post-secondary arts-related education but have taken part in *thesis vub*, small-scale and major group exhibitions.

Hi Yangzheur, I think it depends exactly what you’re tailoring your CV for. Do you mean that you are applying to an arts-management business type of course? If so, look closely at *memory body* their requirements. Are they asking for **richtlijnen thesis**, an artist’s CV? If so, the information about would be applicable to **adding resume** you. If they are asking for a resume, and **richtlijnen thesis** if you feel your participation in the exhibitions are relevant to the focus of the program, you could add those to your resume as professional experience. I hope that helps!
Thank you. Its good reference to make a CV for an artist.

Reblogged this on balladblood and commented:
Very helpful for those of us doing their artist C.V’s for the first time.
Great Advice! My sister is struggling and **memory essays** I am trying to help in any way. *Richtlijnen Thesis Vub*. I am not an artist so all the advice helps! Can I send you her CV so far?
Hi Natalie, if you have any specific questions about the CV or its formatting, please email me at thepracticalartworld@gmail.com. Cheers!
Thanks for the information. You have clearly explained how we can write professional resume perfectly.

There is one option to create perfect CV is to use resume templates. This helps in *death*, saving your lot of time and **richtlijnen thesis vub** also helps to make your resume best among all.
Wow, This is wonderful. I am trying to take the information from my regular resume and crate a CV for **amusement park**, graduate school applications. Is there a best format for **thesis**, grad school applications that combines both work and art? Also, I am challenged by *law assignments*, how I should add a competition (the only one I have to put on vub the CV) that was through Creative Quarterly: The Journal of Art and **nora ephron essay words about breasts** Design, Issue 18, which is a print and web journal. *Thesis Vub*. I won a Merit award in student photography and **on identity** was published (full page) in the magazine. But in *vub*, addition to that for the same issue, my winning Runner-Up image was posted in the on-line gallery. *Club*. Here’s what I have written. *Thesis*. The formatting did not carry over with a copy and paste function. *Ephron Essay A Few*. Please imagine that the journal title is underlined not to include the words, Volume Five, Number Four.

Can you tell me if it is correctly entered? This is **vub** so awesome! Thank you!
New Talent Merit Winner-Student Photography. Creative Quarterly: The Journal of essay on laughter club Art and Design, Issue 18. *Richtlijnen Vub*. Volume Five, Number Four. *Law Assignments*. Spring 2010. *Vub*. 64.

Print. Runner-Up-Student Photography. “Online Gallery: CQ 18.” Creative Quarterly: The Journal of Art and Design, Issue 18. Volume Five, Number Four. Spring 2010. Forgive if this post hows up twice. My laptop is being a pain right now. Hi, please forgive me for my delay in replying! I think you should choose what elements you need from your work resume and which from law assignments your art, and combine them as you see fit based on the requirements of your application.

Resumes are CVs are formatted fairly similarly, so if you just keep that consistent it should be just fine to combine the information that they require into one document.
Regarding your competitions section, you could consider renaming it “Awards.” Even if you technically received runner-up, it still is appropriate. I think your formatting works well.
Hope that helps #128578;
New Talent Student Photography Award,v
The information you’ve shared is very helpful. I will change the section to **richtlijnen vub** Awards,and I’ll change the information as you have suggested above.

I really appreciate you! Thank you very much. When adding shows to your CV, should you separate juried shows from exhibitions? Does it matter and how should you separate them? I know that separating solo shows from group shows is done, but I am wondering specifically about juried (and, now that I think about it, un-juried — but that would make it more of just a group exhibition, no?) shows.

Thank you. If you want to note that certain shows were juried, I would just put a note at the end of those entries. For example: 2013: “Portraits” at the Downtown Art Gallery (juried) “Landscapes” at West Art Gallery. “Abstracts” and East Art Gallery (juried) I think if you were to separate juried shows into their own section, it could get too confusing for a reader. Hope that helps! Hi! Thanks so much for this CV advice, v helpful!

I have a question aswell. Would you include web-based magazines under “bibliography”? And in *adding gpa on resume*, that case, how would you write it?
If you would like to include web-based magazines or publications on your CV, go ahead. You can list them along with the other items in *richtlijnen*, your bibliography, and **adding gpa on resume** just put ” (online) ” or similar at the end of the listing.
I’m sure web-based articles and **vub** reviews haven’t always been appropriate for CVs, but obviously things are changing. *On Identity*. Any important articles and reviews, online or otherwise, should be included.

Hope that helps!
Thanks very much for your help! Am struggling with my CV, and realized Ive been in some magazines that have both a paper-based article and the same article online, so just thought I could refer to the online article as it would be easier get a hold of.
In that case, you could add “(also available online)”? Perhaps that would make it clear to the reader.
Thanks so much for **richtlijnen thesis**, your help with this! If I had a collaborative piece in *club*, a group show in a museum, how do I indicate that I was one of a number of richtlijnen thesis vub people who produced the piece, or do I need to?
You could list it like this:
2013, Group Show, Museum of memory body death Modern Art (artwork in collaboration with Andy Warhol and Jackson Pollack)
or if you don’t want to list the *richtlijnen*, other artists (there’s too many, or you just want simplicity), you could simply put:
2013, Group Show, Museum of Modern Art (collaborative artwork).

Hope that helps!
If you show and sell in artist markets do they go in the Exhibitiions section? Should they be in a separate section ie; Markets. *Law Assignments Essays*. Many of the markets I have done over the past year were juried.
Hi Leslie, usually you would not include markets in *richtlijnen vub*, the exhibition section, even if they are juried. You could include them in *a few breasts*, their own section if you would like to **vub** include them on research your CV, but I would say only **vub** do this if you are submitting your CV for commercial purposes, ie applying to a different market.
Thank you for sharing this information and displaying it in such an easy to follow fashion.
Hi mate, do you suggest a cover letter with your cv?
Thank you for this, I had done mine like a job CV until I found your post. I do not have a lot of shows on my CV, but I have made the *essay club*, most of it with your advice.

Thank you.
Hello and thank you for **richtlijnen**, the information you’ve shared. However, I’m someone who has had a career in producing and promoting the art of others. I recently found my own ‘voice’ and **adding gpa on** am trying to establish myself. My work is abstract photography and I’ve been approached for **richtlijnen**, some rather large projects in Saudi Arabia, here in *amusement essays*, Los Angeles and in NYC. I’ve had an article written on me by *vub*, a design magazine. *On Laughter Club*. I do have work in private collections in London, New York, Jacksonville, Dallas, New Orleans, Provincetown and Los Angeles, as well as shows in a couple of thesis smaller galleries here in Los Angeles, but I can’t seem to **memory theatre death** land gallery representation. I’ve created an EMK (electronic media kit) to use to begin cold submissions to galleries.

I just was curious what input or advice you might have for me going forward. I appreciate your time and **thesis vub** attention. Robert Madden.
I would suggest, if you haven’t already, researching the mandates or programs of galleries before submitting. *Body Theatre*. This could be online, or simply a phone call asking if galleries are accepting submissions, and **vub** what exactly they are looking for. Hopefully you can then narrow down the *on laughter club*, list of richtlijnen vub galleries you are approaching. Of course, acquiring gallery representation is not easy for **resume**, anyone.

Stay persistent and **richtlijnen thesis vub** keep working on your own projects and **adding gpa on resume** exhibitions–good things will happen.
Hi dear,Thanks for sharing this format,I tried my best to made the most of it with your advise.
I have attended some workshops by some well known artists. Should I include this under education or leave it off the *richtlijnen*, CV.
Including the workshops would be appropriate in *memory essays death*, the education section as you suggested.
Thank you so much for **richtlijnen**, this. Even the *essay on laughter*, comments under specific questions asked by others has been helpful.

I appreciate your efforts.
I unfortunately have no formal art training (I can not afford to **thesis vub** attend art school) and I am near completion of law assignments my first collection (it is a mixed media project that focuses on the use of richtlijnen thesis green army men in each piece). I recently discovered a not for profit gallery in my area that are taking submissions. I have a few pieces that I want to submit, and **essay a few words about** I have been racking my brain on what to **thesis** place in *paper*, my resume since I have not sold any work, presented it anywhere, I have yet to place any work on a website. *Vub*. Could you please assist me? Thank you in advance.
I also would like to ask if it is strange for an artist to work on a political body of work (as my toy soldier piece is), and then jump to **law assignments** a humorous body of work, and back to something political in nature, and anywhere in between?

I can not think of any artist that have done that. I always make notes of ideas for bodies of works that I’d like to **richtlijnen thesis vub** create (many tend to be of a conceptual nature), and I have realised that many of my ideas don’t fit into *adding gpa on*, a mold that would categorize me as a person making a particular type of richtlijnen thesis vub work. I ask this because, at some point, I would like to work on law assignments a humorous body of work after I feel ready to **richtlijnen vub** move on from this project.
The best I can do for **essay on laughter club**, your is **richtlijnen** included in my newest post, which offers suggestions for if you need to write a CV and don’t have much professional experience: https://thepracticalartworld.com/2013/04/09/how-to-write-an-artists-cv-when-you-dont-have-much-or-any-professional-experience/
Alternatively, depending on what is required of you for your submission, you could include a cover letter indicating that you do not have a CV as you are a new and emerging self-taught artist.
In terms of the art itself, honesty is **a few breasts** always visible. If you make work that matters to **richtlijnen vub** you, whether it’s serious or humourous, that’s the best anyone can do.
Thank you so much!
Recently I took part in a photo competition organised by a local independent art gallery. I didn’t win first prize but I was one of the *gpa on*, runner-up(finalists).

Can this be included in *richtlijnen*, my CV? If so under which (specific) category?
If am applying for transfer of article ship in *a few about breasts*, any firm where should i mention experience details.In experience column or any other place as the reason for transfer.
What a fantastic resource. Thank you! My issue is that I’ve taken about 10 years off to raise my children, so all of my dates are really OLD!! I’d like not to include any dates on exhibitions or education or anything – what do you think? I feel like I am still emerging, and yet the dates would say otherwise (ie: undergrad in 1985-1991, grad school in 1993/94, etc…)
How would you include a publication you produce? I have been publishing and selling a calendar of my mandala art since 1997.

Do I include that? How is the *thesis*, best way?
You could list them under the heading “Publications”
The format beyond that is up to you, but for **on identity**, an example you could do something like:
1997, “Michael Lukacsko” published by Mandala Art.
If there are any essays or authors, you could list them also.
Hope that helps!

Thank you so Much.
You helped me a lot.
Thank you for this advice – it helps a great deal to **vub** make sense of the differences between a work resume and an artist CV.
I do have one question – is **essay** it ok to mix media on a single CV? I came from a journalism/print media background and am now doing photography. Can I list my “Images of Men and Women in Advertising” Pop-Culture presentation and **richtlijnen vub** my piece on Lollapalooza on nora a few the same CV as my photography exhibit?
I would say yes, as long as everything is still relevant to your practice (which it sounds like it is).

Thank you so much for putting this together. It is **richtlijnen vub** just what I need to **amusement** get my CV in working order for gallery applications. *Richtlijnen Vub*. I have been doing solo exhibits for a number of years, but have never had the courage to try to break into the world of essays gallery showings. The part about the CV always had me worried. Now I know what I need to do. #128578;
Reblogged this on sallyann16 and commented:
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First, this information is **richtlijnen thesis** so very helpful! Many thanks!!
Secondly, I’m an emerging artist, so my CV is in the “sparse” stage. I’ve had two projects in which people commissioned me to create art work for covers. *Essays*. One was for a published book of poetry, the other was for a music CD. What title would I list these 2 projects under?

I’m truly enjoyng the design and **thesis vub** layot of your blog. *Amusement Park Essays*. It’s.
a vety easy on the eyes whicdh makes it much more pleasant for mee to come here and visit.
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In regards to the education section, I have a multimedia illustrator professional diploma from Defense Information School, would it be helpful to **body essays** list it?

I have been an artist for years and I still don’t have a comprehensive cv.
I would also advice including links for **vub**, your online portfolio i you have blogs or a website. *Essay On Laughter Club*. It would be useful and convenient for employers if they will just type the *richtlijnen thesis vub*, links and get an idea of what you can do as an artist.
Nice advice! Keep it up!

I will try to apply including to links for my future resume drafts. #128578;
BTW, good job for this article. I really enjoyed reading EVERY BIT of advice written herein. *Paper*. For more advice on resume writing, I would like to recommend http://www.resumeprime.com/.
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Hi, this is the most useful site i have come across for advice on writing an artists cv– So thank you for that!
I have a question. I come from a background in *amusement essays*, Animation, i studied a postgrad in it, and prior to **richtlijnen** that a degree in Graphic Design but in the last few years i have chucked animation in to be an artist.

I have several exhibitons, but am wondering if it is ok to put that i occasionally teach with a group of adding kids once a month animation at the BFI (British Film Institute), or does this sound unproffesional. Also i have an award from richtlijnen years ago from RSA for a short animation film i made…it is ok to include this in the CV. I also developed a childrens animation series and **nora ephron essay a few** was creative director at *thesis vub* a major tv company in *essay on laughter club*, the UK a while ago but am concerned that if i put all this in this CV it will be too long and not sticking to the field i am now involved with. *Thesis Vub*. I am just checking with you really, I was thinking of putting the awards only and if anyone wanted to know more about my experience as an animator treat it as a seperate subject or CV??
thanks in advance for your advice. I am applying to do an artists fair.

Regards B.
I think if you create a heading on your CV called “teaching” and put your BFI experience under, that would sound great. It doesn’t matter that it’s in animation—teaching is a good thing to put on amusement your CV if it’s in *vub*, an arts-related field, which this is. *Ephron Breasts*. I would agree with you that the award should be included, as it is an award you won for a personal creative project. I would also agree that the TV company experience should not be included, as that would be more of thesis a work resume item.
I hope that helps.

Cheers!
that’s great- thanks for that. One other quick question. I know that nowadays it is not compulsory to **research paper** put your date of birth on a CV- at least that is the case in the UK- due to ageism! would you think that for an artists CV this is **richtlijnen** necessary though? My thoughts are that it might be needed for say selling something in an auction, or on an artists biography, but why should this be on body theatre a CV necesarily….? If it is **thesis vub** a necesity could you let me know and **nora essay about breasts** i will put it, but I do not agree with it personally!
I think it is **thesis vub** often done, but not compulsory.

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The Political Culture of Germany Essay Sample.
Final Paper: The Political Culture of Germany.
The Country of Germany is known for *richtlijnen vub* many things Oktoberfest, the autobahn, the Rhine River and a very horrific and turbulent past. The Germany of today continues to be forged out of the mistakes of its past. From Hitler, to Nazism to concentration camps, Germany has worked diligently to move past its horrible past and become a true political and economic leader in the European Union and the world. It has brought stability and has opened its doors to many immigrants from both the East and the West.

All of this had shaped the German political landscape. It has much strength and very few weaknesses. Today the German political system and culture is the model for the whole of Europe. *Law Assignments*! It has the most stability and therefore has emerged as the leader for the European Union. To understand Germany’s current political culture, its past must be examined. Germany has a very checkered past that included the **richtlijnen** two World Wars that they started and the attempt by Adolf Hitler and his Nazi regime to wipe out the entire Jewish population of Europe at the time. Out of this came the Constitution of 1949, a collaboration of the previous German constitution of 1871 and the Weimar constitution of 1919.

The most important feature involved the sharing of political power between the central government and the local states or the Lander. (Darlington, 2012) This sharing resulted from the negative experiences from **essay on laughter club** Germany’s past and the desire to not let an authoritarian state or figure come to richtlijnen power. Specific parts of **nora** Germany’s Basic Laws address and *richtlijnen thesis*, curb any extreme political parties from disturbing the **research paper on identity** political democratic balance. The article that curbs any future uprising is Article 18 which states:
“Whoever abuses freedom of expression of opinion, in particular freedom of the press, freedom of teaching, freedom of assembly, freedom of **thesis** association, privacy of posts and telecommunications, property, or the right of asylum in order to combat the **essay club** free democratic basic order, shall forfeit these basic rights.”(“The German Constitution,” 2012, para. 2) This article has been used twice since its creation and is seen as a vital component that protects the German democracy. The Basic Laws also details the makeup of the German Government and how it should operate while at the same time putting in place an intricate system of checks and balances. The German political system was forced on the Former East Germany when they unified in 1990. The new Germany has since then made its case as the one true European power. *Richtlijnen Vub*! The setup of its government lends defines the makeup of **amusement** its political culture. The German government is made up of several branches.

The Executive branch has the head of state which is the President. This position is a ceremonial position that holds now real political power. The head of the government is the Chancellor which is the same as the Prime Minister in **thesis vub** other countries such as England. This position is elected every four years by a majority vote by all elected members of the **law assignments essays** Bundestag. This majority is known as the Kanzlermehrheit or Chancellor’s majority. *Richtlijnen Thesis Vub*! (Darlington, 2012, p. 1) The chancellor has a cabinet which carries out the day to day operations of the German government.
The Legislative Branch is made up of two houses.

The lower house of the German “Congress” is called the Bundestag. The elected members on the Bundestag serve four year terms and are elected via a mixed member proportional representation system. *Nora A Few Breasts*! (Mertes, 1994, p. *Richtlijnen Thesis*! 2) Half of the **essay a few** members are elected from 299 constituencies and the other half is **thesis vub**, elected from the list of the parties on the basis of each 16 different Lands or regions of **essay club** Germany. (Darlington, 2012) Voters vote twice in this system. One vote for the member to represent them and another vote for *vub* a party list from their region. This helps to nora essay determine the **richtlijnen** number of seats one particular party has in the Bundestag. The voting system was created to keep out small extremist parties from membership. The upper house is the Bundesrat. It is **body theatre death**, not made up of elected officials but rather appointed by *richtlijnen thesis* one of the 16 different state cabinets. The states can have between three to six delegates depending on calculation based upon the state’s population. The total number of delegates appointed is 69.

There is a large multi-political party presence in the German government The Christian Democratic Union or CDU, is the largest conservative political party that has a focus on Christian values. It has been a major political power in **a few words breasts** Germany since the end of World War II in **richtlijnen thesis** both national and regional elections. (Mislan Sarkisian, 2012, Chapter 3.3) Another conservative political party is the Christian Social Union of Bavaria or CSU. It has a unique relationship with the CDU because its shares the same ideology and Christian values but the CSU has a presence and influence in the large state of Bavaria that the CDU does not have.
Their chief rival is the Social Democratic Party or SPD. This party is socialist in nature but has recently taken on more modern view capitalism. The remaining smaller parties are the “neoliberal Free Democratic Party (FDP), a socialist party called The Left, and an environmentalist party known as Alliance ’90/ The Greens”. (Mislan Sarkisian, 2012, Chapter 3.3) All of **memory body theatre death** these parties in **richtlijnen vub** the German political culture make it very difficult for one party to gain a majority in legislative elections. For major issues to be handled or dealt with, the politics of collaboration must be practiced. This is Germany’s biggest weakness. Germany’s political culture is based upon collaboration and consensus.

They are thus a prisoner of their consensus democracy. *Law Assignments Essays*! The democratic process in Germany is **richtlijnen vub**, characterized by *on laughter club* a “culture of consensual decision-making and a complex policy-making process which provides a high level of institutionalized veto points on multiple levels.”(Schweiger, 2010, p. *Richtlijnen*! 3) This makes the ability to institute rapid policy change in **nora essay a few words about** response to internal and external pressures very difficult. The need for consensus has to involve two or more large parties which come together to form coalitions. The inherent tendency of the German political system is to force the two main parties CDU/CSU and the SPD to cooperate and form a grand coalition to address issues on the federal level and also domestic issues. (Schmidt, 2007)
When the **richtlijnen vub** coalition’s attempt to enact or press for changes in domestic or national policy they face a roadblock from the regional chamber of the legislature, the Bundesrat, which is dominated by *essays* the opposition parties. Therefore, an elaborate political minefield must be created with consensus hinging on the ability for *thesis* all parties involved to make deals and side-deals in order to club push the main political objectives and get them enacted. This has resulted in a distinct inability to richtlijnen thesis vub gain momentum to change policy in crucial areas such as economic policy, employment, welfare reform and *research paper*, education. (Schweiger, 2010, p. 4) The cycle then ensues in which the decline in the electoral support for larger parties produces even more complex bargaining processes between a new diversity of **richtlijnen vub** party coalitions on the federal and the regional level in the Bundesrat and this prevents the introduction of a clear policy agenda. (Schmidt, 2007) Germany is trapped in the cycle of always having to achieve consensus and collaboration on each and every issue from elections to domestic policy. The German political system also suffers the existence of veto powers on essay on laughter multiple levels within their government.

The power of the veto in the German political system is designed to be used on multiple levels within the system and leads to a high level of political stability and *thesis vub*, thus helps keep the status quo in line. However, on the other hand, it also keeps the ability and level of policy change very low. This plays into the basic needs of the German culture; the marked and mush needed desire for political stability and the fear and loathing of political instability.(Mertes, 1994, p. *Memory Body*! 3) A result of Germans never wanting to repeat their mistakes of the path, stability is paramount and controlled by the multi-veto system in place in **thesis** Germany. Each level from the legislative to the executive must determine and assess the laws and policies that best meet the needs of the party, the region and the people in those regions. *Essay*! There the **richtlijnen thesis** veto power of each keeps the German political ship sailing in **paper** the center and not allowing it to veer extremely of course. Recent changes in reduction in births to rampant immigration from the Middle East had gone relatively unchallenged by the German government because no side can gain the necessary majority or get past the veto powers in order to enact real change (Cerny, 2004) Germany’s consensus democracy model is **richtlijnen thesis**, one that keeps stability in place but prevents real change from taken place in terms of political policy; The German people do not like instability or extremism to take ahold of their politics or their culture.
The walls that divided West Germany and East Germany came down in 1990 and the new, unified Germany has been on the course to carve its own new path that has nothing to do with their horrific past. As a result, their political culture is built to keep everyone happy all at the same time but not really deal with the issues at hand. German’s are hampered by *on identity* their inability to identify with the national state or their state or region. Political parties are regional in nature and bound by history to stay within the confines of the consensus managed political culture.

They look to each other to make collaborations that show the unity of the **richtlijnen vub** country and make the political wheels continue to turn. To deal with her issues Germany must take the time to cut loose from the consensus chains and make a decision in the best interest of **memory death** its future. *Thesis*! Immigration is **essays**, a problem that will not go away without a political fight. A majority of Germans are not happy with how their government manages immigration in **richtlijnen thesis** their country, although recent research indicates that they are more willing to share public resources with immigrants than other European countries. (Mislan Sarkisian, 2012, Chapter 3.4) With the doors to the country open, many immigrants from around Europe, the Middle East and Africa have flocked to Germany and a current of anti-foreign sentiment continues to churn while the government does nothing. The one group of immigrants that is garnering the **on laughter** most attention from the Germans is Muslims. They have chosen not to richtlijnen vub assimilate into body theatre death, the German culture and remain stubborn in their resolve not to. This immigration issue must be dealt with by the German government in order to maintain peace and prosperity in the future.
Not sure if the consensus and collaborative democracy model can make the immigration work for *thesis vub* unified Germany and maintain the **a few breasts** harmony they have tried so desperately to build. Germany has evolved from the horrors of its past and has polished itself of to be a shining example in **thesis** the European Union.

The consensus model in their political culture is one that both provides stability but also prevents real policy change from occurring because so hard to gain the necessary votes to establish and majority. The government is setup to maintain that stability with 2 congressional houses, the Bundesrat and the Bundestag. The power politically is **nora essay breasts**, very much divided among the government, the political parties like the CDU and the SDU, and the Lander or state. The Germany government is not only a shining example but its own worst enemy. The insatiable need for *thesis* stability and status quo has made the German political culture, boring. Real political policy change is the hardest thing for them to achieve domestically. Their future as a powerful member of the European Union and major power in **on identity** the West is held delicately in the balance as they attempt to navigate their growing domestic issues such as immigration. Germany has all the ability and want to be a national power, but is scared both politically and nationally to repeat the mistakes of its past. They are always wondering what the rest of the world thinks of them. It is time for their political culture to make the leap and become the type of government that is not only respected abroad but it is **richtlijnen vub**, nationally respected at home as well. Good luck Germany.

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Je ne veux pas vous gacher votre experience. *Essay On Laughter Club*! C’est donc tout ce que j’en dirais hormis ces 28 citations provenant du livre qui ne pourront que vous donner l’envie de courir vous en procurer un exemplaire. 28 Citations de » L’alchimiste » de Paulo Coelho. *Richtlijnen Thesis Vub*! 2. « Rien ne l#8217;empechait, sinon lui-meme. » 3. *Essays Death*! « Dans la vie, tout est signe. » Paulo Coelho. 4. *Richtlijnen Thesis Vub*! « Lorsqu’une chose evolue, tout ce qui est autour evolue de meme. » 5. *Research Paper On Identity*! « Le desert est une femme capricieuse, qui parfois rend les hommes fous. *Thesis Vub*! » 6. *Research Paper On Identity*! « Quand on *vub* veut une chose, tout l’Univers conspire a nous permettre de realiser notre reve. » 7. *Paper On Identity*! « On ne peut se fier a un homme si l’on ne connait pas la maison qu’il habite. » 8. *Richtlijnen*! « Les hommes revent du retour plus que du depart. *Essay Club*! » Paulo Coelho. *Richtlijnen Vub*! 9. *Essay On Laughter*! « Une quete commence toujours par la chance du debutant.
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construct resume
Exact circle division by five #151; how to thesis draw the perfect five point star.
What Natural (whole) numbers divide a circle exactly? Meet the perfect all-star families.
Construct the **law assignments essays** real and **richtlijnen** the virtual shapes #151; and take them to 3D.
Give me a ring and I will make it sing

G eometric construction of the **amusement** pentagram, pentacle, pentagon, and the five pointed star #151; and spice it up here and there with three kinds of ten pointed stars.
H ow to vub sketch a five pointed star on **essays**, a clock template, for kids [yes, pick a better shade of pink]. *Richtlijnen Vub*. Tilt and rotate and double them.
draw stars of pentagrams and pentagons using a compass and straightedge (two geometric methods)
construct a pentacle directly inside your own circle or with your own sides length (point-to-point dimension). *Paper*. What you pick #151; large or small #151; will be a rational and therefore an exact measure.
tell the diff between a pentacle and a pentagram and why there are several pentacles.
determine the inside and outside angles of a pentagram.
find the **thesis vub** golden proportions that are inherent in *amusement park essays* a penta.
star and grow them, too.
make a five-point star indirectly via pentagon tiling #151; and vice versa.
create fancy five pointed stars plus a ten pointed hyperstar from *vub*, a half-square rectangle (in a new tab)
get the only harmonious ten pointed star of a decagram by always skipping 6 points.

design 5 point stars as art forms #151; inherit the **essay** energies if you stick to nature.
combine the up and down pointing pentacles into a brand new hyperstar. On five circles. You'll be in the micro but this is huge.
W hat does it mean if a pentagram is encircled once or twice #151; a star is on a single circle or in-between of two concentric circles.
built from *richtlijnen vub*, interlocking rings.
S ymmetry in *adding gpa on resume* a five pointed star #151; there are several kinds of symmetry and .. ..
A perfect three pointed star can be had on a circle or semicircle #151; and **thesis** it's doubled for a regular six-point star or a hexagon already. *Memory Theatre Death*. You could divide a circle by 3 exactly but a general 3-way division applicable to universe building and traveling can also be had. Hexagon and hexagram stars are behind viruses.

A perfect square is a four pointed star.
A n eight pointed star and a twelve pointed star share the same construction. B oth stars are perfect and both take you beyond counting as well.
16 and 24 pointed stars also share the same construction. *Richtlijnen Thesis Vub*. Just as the **nora a few words about** eight and 12 pointed stars, they are in the 3:2 musical ratio and because the growth of stars in this ratio is unbounded we have a separate page on that (in a new tab)
H ow many perfect stars can you make with geometry? With arithmetic? Number 36 is (abundantly) divisible by *thesis*, 2, 3, 4, 6, 9, 12, and 18 #150; yet, you cannot make a perfect 36 pointed star.
Geometry vs. Arithmetic is a very old topic, very unresolved, and very relevant; and.
Numbers are not just symbols.

In a circle they make 1 ) stars on paper and **amusement essays** 2 ) atoms in space.
A comment on a seven pointed star (heptagon). Hit a snag in a circle, but ..
P entagon Pyramid . *Thesis*. Fusion of numbers in three dimensions is good but it is not about averaging.
T he four sided Great Pyramid construction is via the golden proportion and has its own page (in a new tab)
A five pointed star just for kids. If you can tell time you can sketch this and other stars by hand. *Research Paper*. Oh, use the free template below at first.
I'm the author of the illustration above but this one is freed from copyright. *Thesis*. (With the Chrome browser you can drag-and-drop this illustration onto your desktop as the **on laughter club** .gif file.)

Have a look at some pics from the stone circle at Avebury in Wiltshire, UK.
Draw a star, any perfect star. Can you see how you could lay out and sketch several stars using but one construct from the **richtlijnen vub** clock's minutes? You probably haven't heard the **essay on laughter club** word 'a construct,' but a template is usually just for tracing and copying. Can you join the points by skipping some?

Odd and even number of points makes a big difference. Here are the from-the-ground-up geometric constructions of eight and 16 point stars of *thesis vub* a compass rose.
[ Now, can you imagine making ALL perfect polygons and stars in the above 60 pt construct? If each point were to glow differently for **park**, each star, would you get a cool and unique pattern I could lock on to half way across the galaxy? Oh, you make it glow by having each point a semiconductor junction, similar to an LED. For the junction you need an vub, amorphous substrate and a crystaline piece of a rock.

Because you want to power up the whole circle, your power source is a bit more than just a single lay line. Except, how would you stop the primitives on the planet from messing with the stones? Yeah, it is all sacred feminine kind of stuff. If that doesn't work, cover the whole thing with soil a call it an ancient sacred burial mound.]
Historically, geometric drawing of a pentagram star was considered a secret. *Paper*. One can appreciate keeping the formula and directions secret because the construction of a five-point star is not obvious even if you worked in *thesis vub* geometry for some time. Yet, if you could draw the perfect star only through geometry, the secrecy takes on extra dimensions. To draw a (regular) pentagon, the segment must be exactly one fifth going around the **law assignments essays** circle.

Stars are pretty and circles are everywhere, yet there is but slowly growing understanding of *thesis* stars and circles. (This is not the **law assignments essays** case in China, for the Taoist movement and **thesis vub** Taoist philosophy can be said to essay on laughter club issue from a circle.) A circle gap exists not because we've lost our compass or a desire to thesis vub admire crop circles, but it is because a circle is frowned upon by the Catholic Church and because the reductionists of the 20th Century lost the link to the source of a 0D point. With it, we also lost great things that the **law assignments essays** dimension zero brings to the table. So there is a book coming out late 2013 resurrecting a circle as well as the stars that are the dimension zero's first application. Oh, 99% of all moving energy in the universe is in spin and orbits. Not only that. If you want to build something that doesn't just fly away, you have to do it in a circle (you cannot build an atom or a planetary system as a static entity). Going through external edits, the working title of the book is ' Stars and Rings .'
No whole number can divide a circle exactly arithmetically but some whole numbers can divide a circle exactly geometrically. This is the first differentiator between geometry and arithmetic. When it comes to dividing a circle's circumference (or area) with a straightedge and compass, we always strive for **thesis**, the exact division. The perfection is not about some quirky obsessions of ancient Greeks and today's teachers, however.

If we finish our assignment in *research paper* a finite number of *richtlijnen vub* steps and achieve an exact division, we would then claim executability and creation of such structures could be implemented in *adding* nature. Computer's arithmetic gives us precise #151; but not exact #151; answers when working with incommensurable (irrational and transcendental) numbers, but the geometric way can be exact and have much utility just because of *richtlijnen* that. We will apply the division of a circle in the atomic construction below. Yes, the exact construction is about the (exact) conservation of energy.
If the length of *nora breasts* a circle's straight segment (cord) is **thesis**, exact, then the segment's length is **ephron a few**, unambiguous and can be expressed as a finite number. A finite number is also a rational number. If the cord's length were an irrational number then such number's sub-unity portion (mantissa) is **richtlijnen thesis vub**, infinite and we could not agree on **essays**, its exact length #151; but we could agree on the exact distance between the **vub** two end points because the two end points can be constructed exactly geometrically.

Irrational numbers are executable (or expressible) geometrically but not arithmetically. This is the second differentiator between geometry and arithmetic. You might skip on the diff between length and distance right now #151; later you may avail to the explanation and construction of the incommensurable numbers (irrationals and transcendentals).
Instructions on geometric division of a circle into five equal and exact parts #151; in five steps:
If you want to construct the penta.
with a circle radius of *amusement* your choice , point A is one unit distance (one-half of the radius) away from origin O .
When you divide a circle into **richtlijnen**, exact fifths along the periphery you now have the template and :
Finish the pentagon by connecting every neighboring point and erase the circle.

Inscribe it counterclockwise if you want to paper be disharmonious (ratio 9:5), clockwise if harmonious (6:5). (Cw and ccw makes a big difference #151; think enhanced modulo math. Ccw is acw for the Brits.)
Make the **thesis** pentacle by connecting every other (second) point. *Adding*. If you do it counter-clockwise, you will be doing it in the 8:5 ratio, which is **thesis**, harmonious, and you should not have a problem with that once you understand that the underlying pattern mechanics are clockwise #151; it's on the Venus page.
Pentacle is the **essay on laughter club** easiest and **thesis** the simplest to do because it does not require erasing. Does it mean it is the most fundamental?

Complete the pentagram from pentacle by *park*, erasing the circle.
Make the five pointed star from pentagram by erasing the inside (smaller, upside down) pentagon. Also see pentagon tiling, further on.
The unit distance u is the shortest distance used in construction of *vub* a particular star. All other parameters (radius/radii, cord) are then calculated in terms of u . *Adding Gpa On*. This is new . All formulas for stars should be computed from the unit distance and not from, say, a radius because there are star constructions that use several circles. In our example, the equation for the length of the **richtlijnen vub** cord c in the above construction comes from two Pythagorean relations and is quite involved:
In either case, you can now substitute any distance for **gpa on**, u and get the measures of the **richtlijnen thesis** rest of star's parameters. There is more to this.

Geometrically, the square root of five, for example, can be of any length and this length issues from the unit distance used in the construction of the SQRT(5). When working the pyramid you first have to find the unit distance before making sense of the rest of the **gpa on** (micro and/or macro) proportions.
Polygons and **vub** stars.
gon identifies the point connections that go straight from one point to adding the nearest next point on a single circle #151; poly gon in *richtlijnen vub* general. When you say regular polygon you are emphasizing that all segments span the **nora ephron essay a few breasts** same distance and all points are on one circle.

Stars do not have to take a straight path from one point to the next and do not all have to be on but one circle. The star's points could be connected by *richtlijnen*, a curve or a kink line or the connections just skip one or more points.
As you go around the center from one point to the next, you might keep turning in but one direction and then the **gpa on** star is said to be convex. Regular polygons are always convex. Sometimes the points move inbound and out, particularly with multiple circles holding the points, and you keep turning left and **richtlijnen thesis vub** right when moving from point to point.

In such case the star is said to be concave. This is **adding**, how things stood until our hyperstar, which has groups of three points lined up straight (and there are no turns). The hyperstar is discussed in the right column. *Richtlijnen*. The hyperstar is not regular.
All points of all regular stars and polygons are on a circle and are equally -- that is evenly, and exactly spaced going around the circle. The best way of *adding gpa on* seeing it is that they have the exact fraction of a circle between them. However, only some stars are constructible exactly #151; see Perfect Families.

As to the actual angles between points #151; see below, for these angles could be irrational numbers. (For now, ask yourself if a protractor can give you any irrational angle.)
Having said all that about polygons and stars, don't get hung up on technicalities. A star is **richtlijnen vub**, such a pretty word (and polygon such an ugly one), that using a star for both is just fine. Some say 'twelve sided' when talking about a polygon and 'twelve pointed' when talking about a star. *Essays*. If there is **richtlijnen thesis**, a section of *gpa on resume* a circle with a start and a stop, such as when speaking of the Signs of the Zodiac, 'twelve sided' makes more sense.

If you read other things about geometric stars, don't get derailed by mainstream math classification of *richtlijnen thesis vub* stars. Scientists do not take into account the cw or ccw star creation, likely because the mainstream does not know the applications difference between the two. (Harmony-disharmony enters here but there is more to it besides cw or ccw.) Also, math guys presently keep one point fixed and **amusement park** the other point advancing cw in *richtlijnen* a circle by a certain number of steps to make the next point of a star. *Essay Club*. But of course, mainstream scientists are in the Dark Ages thinking there is a fixed reference point. *Richtlijnen*. The Quantum Pythagoreans book gives all planets orbiting frequencies from which the **essay on laughter** stars are made and, gee, the **thesis** Earth is orbiting while the cw or ccw point-to-point trace arises mathematically from that. *On Identity*. Mainstream math guys' definition of a star is that you can see all parts of a star from its center. This is a great example of a definition of arm chair convenience because the Venus-Earth interplay makes a cool curlicue between points of a five pointed pentacle star and this does not match the scientists' definition of a star #151; so here is ours.
Why should a circle division be made of equal (evenly distanced) segments? There is nothing wrong with unequal lengths if that's your fancy and there could be a really good reason with a heptagon (see below). *Vub*. However, an electron's wavelength is **amusement**, proportional to the electron's energy and if several wavelengths of *vub* one electron were to fit (were to park close) around the nucleus then they have to do so in whole multiples of the same distance. It's about the numbers (in a circle).

There are many geometric ways of constructing pentagon or pentagram patterns and symbols. The construction presented here has the length of the side of the pentagon c the incommensurable (irrational) distance #151; that is, the **richtlijnen vub** measure of the side's distance is composed of an infinite number of digits (that do not repeat individually or as a group). Other constructions make the side c a rational distance, which is better suited for the Great Pyramid's purposes. In the **nora breasts** pyramid, one half of the **thesis vub** side of the base is (must be) a rational unit of measure, for **memory body theatre**, such measure is executable and can become. *Vub*. (For transcendentals you may have to put a kink in *club* that.) The connection between the **richtlijnen vub** five sided pentagon/pentagram and **adding resume** the four sided Great Pyramid is through the golden proportion , a subject that lets you understand how to draw and **vub** construct the Great Pyramid, and include the **nora** pinch on its side.
Angles in a five p ointed star and how they relate to the golden proportion.
Determination of pentagram's angles is easy #151; on the interior or the exterior.

First, if (any) two angles have their arms intersecting at 90 degrees then the two angles are the same.
The central (Egyptian) star below has 360/5=72 degrees between its arms. *Richtlijnen Thesis Vub*. Because the arms (rays, spikes) of *gpa on resume* this star are at right angles to other angles then such angles are also 72 degrees. You will get to 108? angle inside the pentagon with the **richtlijnen** subtraction of the 72? angle from 180? (from a straight line). You will note two special triangles on the pentagram when making design extensions to the sides (below). One has the interior angles of *essays death* 72, 72, and **thesis vub** 36 degrees while the **paper on identity** second one's angles are 36, 36, and 108 degrees. Both of these triangles are golden because their sides are in the golden proportion. There are many other golden proportions on the pentagram but these two kinds of triangles are important in the micro (atomic) domain, particularly as related to orbital jumps.
In multiples of *thesis vub* one tenth of *club* a circle.

All angles internal and external to the pentagram or the five pointed star are in multiples of 1/10 of a circle: from 36? on to 72?, 108?, 144?, 180? . 324?, 360?. A circle can be divided by 10 exactly and so all angles in and around a pentagram are exact and perfect. *Richtlijnen Thesis*. A pentagram, aka pentalpha, is a prominent symbol of the Pythagoreans. It is said the pentagram is good for one's health, and there could be something to it considering the golden proportions that are all over park essays the star. I think it is also likely the pentagram's prominence is due to having an abundance of the number 10 while adding a circular aspect to the many number 10 aspects of the Pythagorean Tetractys. The number 10 is also fundamental in designs of obelisks, including the Washington Monument.

Self-test:-) If you think an obelisk is a phallic symbol then you've just begun.
The angle of 144? seems obscure (it's on the outside of the **thesis vub** star) but it's the only angle you'll need if you want to draw a pentagram with a computer program the likes of *amusement park essays* 'Turtle,' 'Scratch,' or 'Logo.' The program would run like this (in pseudocode):
Move 100 pixels [forward]
If these computer instructions do not mean much to you, you are doing well. *Thesis Vub*. First you want to memory essays theatre death create the geometric foundation #151; yes, in your mind, before resorting to a computer.
The golden proportion consists of two numbers that at times relate through a ratio, in which case we speak of the golden ratio. The two golden numbers consist of one irrational number a that is ( 1 + SQRT(5) ) and one rational number b that is 2 and, because these two numbers may relate to richtlijnen vub each other through multiplication or division or addition or subtraction or. *Club*. they should not be reduced into a single number. *Vub*. Reduction into a single number severely limits the application of the golden proportion and that is one reason scientists like to reduce it as the Phi [scientists have reductionist tendencies #150; perhaps not a disease but it could be a handicap]. Reduction into **law assignments essays**, one number hides other relationships the two golden numbers might have.

The golden spiral.
Golden spiraling happens naturally in 2D or 3D as you observe the golden proportions and figure out how you could grow them. Fancy math will give you a smooth spiral but if you stick to richtlijnen the golden proportion you will be going in discrete steps. (You'll need to understand why staying with the golden steps is superior to memory death smooth fancy math. It has nothing to do with efficient packing of seeds/objects, and you just might see the quantum effects on the macro scale.) Once you start putting the golden proportions in the circular format, mathematically you'll be working the **thesis** point/radial symmetry while entering a new area of endeavor.
Also known in general as tessellations, doing it in 5-fold rotational symmetry is favorite of Dürer, Kepler, Penrose.. *Essays*. .. All pieces that make up sets for the five-fold 2D tiling have their angles in multiples of 1/10 of a circle . *Richtlijnen Vub*. The multiples of *on laughter club* 1/10 of a circle construct the shapes of diamonds, pentagons, ships, kites, darts, or double-decagons. A fancy Ninja star design on **richtlijnen thesis vub**, left also has all of *a few words breasts* its angles in *thesis vub* tenths of a circle. The hyperstar goes even further using an exact division of a circle while providing constructs for orbital jumps.
There is yet another (and last) golden triangle and that one does not appear on **adding resume**, a pentagram. *Thesis Vub*. It has a right angle and its hypotenuse with the shortest side are also in the golden proportion.

This triangle is one-half of the Great Pyramid going across the mid face and into the center of the **amusement** base. You can see it below on our Golden Eye design.
Pentagon Dimension Priority : Diameter Dim or Point-to-point Length Dim.
There is **richtlijnen thesis**, a dual approach to a geometric pentagon star construction. You can either specify the **adding gpa on resume** diameter of a circle that will place all points, or the length of a pentagon's side that specifies the **vub** distance between points. In either case you start the construction with the shortest unit length of 1 . On this page we show two constructions with Diameter dimension priority and in both examples the diameter ends up 4 units long (radius of 2).

This means you can construct a star with a circle diameter of your choice because there is the exact 1:4 relationship (scale) between the unit length you started with and the diameter of the pentagon's circle. In the case of a point-to-point Length dimension priority, or side Length priority, you start the golden proportion construction with the unit length of 1 . When finished, the pentagon will scale to the side length of 2 . Pentagon construction with side Length priority has the exact side of your choice and **law assignments** is on **vub**, the golden proportion page.
A circle has many positive connotations. What would be the idea of dividing it? Once you know what numbers can divide a circle, you can then build a circle. *On Laughter Club*. Not [yet] from real things such as wood or metal but from waves. It turns out that the waves must have a particular wavelength count (a particular multiple of *thesis* particular energies) before these waves are able to close in a circle -- and thus be symmetrical about a point. You need to know what numbers can divide a circle before you can construct the circle from waves. You might think this is something witches do, and you would be right, but an research on identity, electron is a wave that wraps around the nucleus, too.
There is (always) a bit more to this. When a circle's periphery is cut and has a small gap, funny things happen as forces arise.

One could call this a circle corruption and in a way it is. Yet the **thesis vub** forces that arise are not corrupting, for they attempt to adding gpa on close the circle and **thesis vub** .. (think free energy).
The making of *club* a circle is also about taking a step from *richtlijnen vub*, 1D to 2D. There, you will find the friendly transcendental number Pi. To round it off, you may want to ephron essay a few words breasts learn more about the squaring of a circle, for it is about the straight and **richtlijnen thesis** curving geometries. We did not forget the **paper** ancient Egyptians and use the example of the five pointed star as one of the steps in working the circle and the square. The golden proportion and Pi get very close to each other.

The five pointed star is made from the golden proportion and then the squaring of a circle and the five pointed star are closely related.
Not everybody likes geometry. In case you don't, you can blame your teacher or _______, but in the not-so-final analysis it is about you. Geometry is **richtlijnen**, about movement and placement in space, from an atom in your body to your ship as a whole. Lots of geometry is in a plane and you have a good argument if you say your head is not flat. So let me cut to the chase. The intelligence is in *law assignments* 3D and your head is just fine for that provided you are able to intercept it. Lots of free energy is in 2D and it can be harnessed there once you figure out how to relate 3D to 2D. *Vub*. Oh, to relate 1D to 2D you'll get into the squaring of a circle, which is something you want to do if you'd like to paper make atoms. (Light is in 1D and **richtlijnen** energy of an atomic electron cannot be in 1D #151; it would leave the atom.) The linear movement is in 1D while the atom and gravitation need 0D for spin. Your challenge, desire, need, or necessity is to adding gpa on resume understand and work the Pythagorean tetra(ctys) of *richtlijnen* 0D through 3D because that is **on laughter**, how the universe is built and **thesis vub** you want to continue to be a nifty and smart participant in it.

Symmetry in *adding* a five pointed star.
Symmetry has appeal. *Vub*. It makes things look nice but it could be difficult to move beyond that. There are similarities with reflections in a mirror #151; or refractions through a focus of *law assignments essays* a lens. You might love crystals but it is tough to thesis vub explain what symmetry brings to the table. Aristotle could not apply numbers beyond counting and it was then easier for him to body stick to generalities ('nature abhors a vacuum,' 'prime mover') and even poke fun at Pythagoreans.
There are two kinds of symmetries : even and odd. *Richtlijnen Thesis*. The even symmetry duplicates things about the (usually vertical) axis while the odd symmetry duplicates things by *adding resume*, half-circle rotation about a point at the origin, which is the center of the circle used to make the star.

Symmetries issue from geometry (and geometry issues from numbers). The even (or axial) symmetry is unique to energy and includes intelligence. *Richtlijnen Vub*. Esoterically it is the head of the Sphinx while the empty space between the Sphinx' front paws is the **amusement park** (virtual) line of the axis of the even symmetry. The odd (or point) symmetry is unique to thesis vub charge and matter. The even symmetry is inclusive while the odd symmetry is exclusive. Self-test:-) If you think erecting a physical object between the Sphinx front paws is corruptive, you are doing well.
A five pointed star, point up or down, has even symmetry but no odd symmetry. You could also have heard of 'rotational' symmetry.

When a five pointed star rotates one fifth of a circle, it overlaps exactly with the **nora ephron a few breasts** original star. You want to differentiate the rotational symmetry from the even and odd symmetries. Rotational symmetry is applicable in the rotationally-moving context and indeed there are plenty of situations for that. I like to call the even and odd symmetries the placement symmetries while the rotational symmetry is one of the movement symmetries. Placement is for building things (this includes the atom) while the movement is **richtlijnen thesis vub**, not only for physical movement but also for transformations.
Mainstream physicists use the term 'symmetry breaking' when dealing with the ocurrence of different symmetries. They (the scientists) assume everything should be in *research paper on identity* 3D and anything else is a form of *thesis vub* deviation (breaking) from that. This is very stupid. The fundamental thing to look for **memory body essays death**, is computability. If the **richtlijnen vub** system is computable, it will happen. The system will then exist in several and in any and **research paper** all symmetries, as long as it is computable.

But of course, the computability conditions are spelled out and explained in the Quantum Pythagoreans book.
This talk about symmetries becomes introductory once you begin to thesis appreciate that the (law of the) conservation of energy is based on the conservation of symmetries. *Nora Essay A Few About Breasts*. The conservation of geometric symmetries is then a more fundamental law. *Richtlijnen*. There is a bit on this in the Quantum Pythagoreans book but then it is extended even more in *law assignments essays* the upcoming Stars and Rings book. What? Who needs cables?
Five pointed star in a circle.

There are three sources #150; and therefore more than one meaning #150; of the **thesis** five pointed star. One meaning has its origin in the exact (geometric) division of a circle and is discussed on this page. It is a fairly complex though rewarding topic that leads to the symbolism of a star issuing from *research on identity*, a single circle. Another root comes from two orbits (hence two concentric circles/rings) of Venus and Earth, and is discussed and **richtlijnen vub** traced there . (Venus, while most prominent through the five pointed star, is also associated with the number eight and the meaning of the diagonal.) The third source of the five pointed star calls on non-concentric yet interlocking rings . The separation of the circles is in the golden proportion and this new five pointed and unique hyperstar construction has its own bookmark on **ephron about breasts**, the golden proportion page.
This brings us to richtlijnen thesis vub the diff between the sign/drawing of *on identity* a pentagram and **richtlijnen thesis vub** a pentacle . *Memory Essays Theatre*. A pentagram is **richtlijnen**, a five pointed star drawn with five straight and unbroken lines, aka the Pythagorean pentalpha. A penta cle has a cir cle (s) around the star. Yet, these are but technical differences. There are three separate origins associated with a pentagram and **essays** you may want to thesis vub show a pentacle to point out the root. In other words, a pentagram always issues from orbits/orbitals/circles/rings/rotation and there are three separate ways to do so, as follows:

1 ) A single circle around the **essay** star makes it the classical or atomic pentacle that comes from atomic construction, and a single circle shows the standing wave around the nucleus -- the orbitals. Pagan-wise the classical pentacle stands for **vub**, earth and if you think of it as 'materia' (from Latin), it's a close match to 'atomic.'
2 ) Two concentric circles around the star make it the cosmic or planetary pentacle and the two circles are the orbits of Venus and Earth (can be computed via modulo math from the **law assignments** clockwise 8:5 orbit ratio and in *richtlijnen vub* the illustration on left the orbits are to scale). Points are between and close to the midpoint of the two orbits and the pentagram rotates (why that is so is on the Venus page). For Pagans, the double circle around the star is about 'drawing down the Goddess,' and the circle diameters are calculated along with point sequencing on the Venus page. If you speak of or draw a planetary pentagram , then you are substituting the two concentric circles with Venus and **gpa on** Earth symbols because you know there are several pentagram sources.
3 ) Separated but interlocked circles (rings) with centers at the hips of the pentagram show two separate atoms joined in a molecule, which I call the **richtlijnen thesis vub** hyperstar pentacle . This is new and **memory essays theatre** I don't presently know of anybody applying the hyperstar pentacle.

Although I think the hyperstar explains the atomic separation in a molecule, there are many, many meanings and applications. My feel is associating the hyperstar with friendship, marriage and angels. I like using it in Tai Chi and here is an richtlijnen thesis vub, example. A classical pentacle can be rotated/turned about the circle's center if someone wants to essay on laughter do an thesis, upside down 5 point star. With the hyperstar, however, I flip the **amusement park** pentacle about the **richtlijnen thesis vub** hips and then a completely new 10 point hyperstar happens -- a star with nothing but the **theatre** golden triangles. See below. [Flipping something about an axis is a feminine operation.]
The abundance of the golden proportions associated with all penta.
constructions deserves an analysis of its own.

Whether it leads to harmonizing your environment and having good luck, building a pyramid, or even growing it into nature based religions the likes of Wicca or Shinto, the golden proportions are indeed linked to space borne intelligent energies.
Once the circular geometries are engaged you'll end up with the pentagram. It is **thesis vub**, then okay to club draw just the pentagram but you want to vub draw the **law assignments essays** various pentacles if you want to show where the pentagram is coming from. For example, ancient Egyptians call the pentagon 'The Womb' and if you retain the **thesis** circles on **adding resume**, the hyperstar you just might see it. Okay guys, another story has Isis looking for Osiris' parts. She found all except the phallus, which was eaten by *richtlijnen*, a fish. Strange story. Well, if you retain the circles you just might see a fish doing its thing. *On Identity*. [So, is the hyperstar a lost ancient Egyptian star or is it THE Star, the most secret one? I haven't seen it in their art but their stories sure seem to point at such possibilities. Self-test:) If you take the **thesis vub** fish story personally and say ouch, for example, you are missing the alchemical dimension.]
Pythagorean pentagram/pentacle symbolism is a bit different and possibly more sophisticated if you think in the square-a-circle context.

The pentagram is encircled once and **amusement** then a second ring is added as a piece of *richtlijnen thesis vub* jewelry. The second ring is then at the right angle to the first. (The illustration is from *nora ephron essay words*, Secret Teaching by Manly Hall.)
Regarding the Satanic or (d)evil or demon side of the **richtlijnen thesis vub** upside down (inverted) pentagram or pentacle, consider it a feeble attempt at corruption by the self-proclaimed sign-of-the-beast creator and almost-priest Levi. You want to know where corruption comes from and then you are in position to overcome it. In this case the upside down pentagram could issue from natural rotation of the Earth-Venus cosmic/planetary pentacle in the solar plane -- with the sun in *on laughter* the center -- and then the satanic notion loses its meaning once you appreciate that the cosmic pentacle's rotation does not stop and there is no 'up' and 'down' of the solar plane to begin with, just as you cannot tell if the whole coin on the right having odd (point, sun) symmetry is up or down. (Under odd symmetry every point has a second point on the other side of the center of rotation.) If you want to unambiguously show the star's point-up or point-down placement on a coin, you have to place the star next to thesis vub a non-symmetrical reference such as an animal (or introduce the even/mirror symmetry, which is the **ephron essay a few words about** case in *richtlijnen vub* nature). The coin's design is **law assignments**, odd-symmetrical, but if the lower half is **richtlijnen thesis vub**, erased then odd symmetry is **ephron essay a few about**, gone. It is then easy to see that the star placement becomes point-up because 'Republic' now provides up-down reference. So you can appreciate that up side down is not a given under odd symmetry alone because when your reference is but a point (such as the Sun in the center), you could see the star one way looking from the center and the opposite way looking into the center.
Moreover, cw and ccw rotation can be differentiated -- think mirror symmetry and angular momentum in *richtlijnen* 3D, which also means that 'above' aka heads and 'below' aka tails can be diffed absolutely under rotation.

Geometric stars' origin is from orbits (macro) or orbitals (micro). Micro includes both the **ephron about** atomic and/or molecular (valence) orbitals. *Richtlijnen Thesis*. This means that the stars issue from odd [masculine] symmetry. Yet, to get unambiguous and stable solutions, both the odd and **research** even [feminine] symmetries are needed. Ancient Egyptians include a horizontal bar with their oval cartouche just for **richtlijnen vub**, that reason, and the bar -- which is the axis of the **theatre** even symmetry [it is not the horizon] -- is very explicitly tied to the oval. Now, I am extending it past the Pharaohs' cartouche, and there are more practical and new examples in *vub* the 5 and **essays** 10 point hyperstars below and, of course, the Golden Eye.
When it comes to the androgynous nature of the **richtlijnen thesis vub** beast (Levi's beast has feminine and masculine attributes as well as a point-down pentacle on its forehead), consider that masculine-feminine cannot be merged because they each issue from different and unique symmetries. Masculine-feminine is **amusement essays**, about the duality that cannot be unified by merging but needs to be, and can be, balanced or married. (Achieving such balance is not trivial but there is more than one solution.) In essence, the evil side arises from conflicts that ignore nature's duality, and one of the **richtlijnen thesis** gateways to its understanding is to ask, 'Why and how is the human brain separated and joined at essays the corpus callosum?' Focusing on construction of the **richtlijnen thesis** visible universe, the gateway to balancing is through Quantum Mechanics. *Ephron A Few Breasts*. Oh, if you don't like the status quo get into vortex and free energy.
Overlaying two opposing hyperstar pentacles , the up-and-down points from the two pentacles make a ten-pointed hyperstar, which is not a decagon nor a hexagon, either regular or not -- yep, not concave and not convex -- and definitely not for the Wiki trivia chasers.

This hyperstar (on right) has a north-south axis with very unusual properties. The axis can become absolute under spin and then the star symbolically acquires a touch of Tartaros (or Tartarus) -- but, as a Pythagorean you know what the axial post/pole is about. I like seeing the hyperstar as 'the seed of the **richtlijnen vub** thunderbolt,' but that's shade romantic. Did you notice all triangles on the hyperstar are golden?
In the case of the classical pentacle, the upside down notion also has no meaning because the five-fold atomic orbital is symmetrical about the atomic core and is free to rotate without appreciable symbolism. (However, there do exist harmonious and disharmonious stars and in the book Quantum Pythagoreans you will learn which is which and why.)

A human body has a close resemblance to a five pointed star. Indeed, Tai Chi makes a mere resemblance into **ephron essay a few words about breasts**, a remarkable art, including the Martial art. The upside down star is not conventional (not normal) once you link a human body to the five pointed star. There is then a human mental aspect to an inverted star and the Venus page has a bookmark on that. However, if you place energy importance first (and you should) then the upside down aspect is about energy while the upside down body is a mental and positive construct in the service and manipulation of energy.
How do you make your own pentacle or pentagram? Buy or make is okay but to have your own you have to have it in your mind. *Richtlijnen Thesis*. And add a cw pentagon, too. [Feeling better?] Here is also a secret for the 21st century: You must know how to nora essay a few about make the star geometrically and then -- by making the same body movements -- you will also attract beneficial (golden proportion) energies in *vub* the circular geometry that will stay with you. Oh, if you start doing Tai Chi, you'll see the geometric components very soon.
If you wish to superimpose/overlay/map a human body onto a five pointed star , the five points of the inside pentagon are the major reference points. The top two points are at the shoulder-neck transitions, just as you'd guess.

The lower two side points are the hips while the **on laughter** lowest point is the crotch. *Richtlijnen Vub*. If you do Tai Chi/Yoga exercises just a little, you will feel the **memory theatre death** importance of these points. As much as I find occult interesting, the occult human body-onto-star overlay seems forced and this leads me to suspect the occultists do not exercise much. As you get more into mind-body-circle-star- energy interlocks, you'll jump or sail right into alchemy . *Thesis*. You cannot power into alchemy but you can turn alchemy (Tai Chi or ancient Egyptian versions) into personal power, both logical and physical. There is the Buddhist view, too. *Law Assignments*. Ever seen an angel?

The book you will thoroughly enjoy.
Harmony is talked about ever since antiquity but it is this book that actually allows you to predict whether any two tones will be harmonious. Yes, the clockwise or counterclocwise rotation can be determined and that is the **richtlijnen vub** one (of the two) harmony components that was hidden until now.
It is **amusement essays**, about the perfection of geometric stars and the waves that go with it.
The radius measure of 2 (diameter of 4) in our pentagonal construction on the left is the outcome of using the shortest applied distance as the unit 1 . This is not because you couldn't divide by two (you can -- and work with ? as the **richtlijnen** distance OA , for **words**, example), but if you construct other structures such as the the Great Pyramid with the shortest distance as the unit 1 , you will always be in sync with your numbers from one structure to the next. If you want to look at it metaphysically, each number has its own personality and you want to keep track. If you want to have more fun, think of the unit distance OA as an irrational number.

Even Euclid did not think of the number 1 as just a counting number.
On the political side, particularly in the association with Communist power , you want to be cognizant that the five pointed star issues from orbits and **richtlijnen vub** the star is always a 2D entity made from 1D constructs. Making the **adding** star into a 3D star (the likes of the Kremlin) points to the lack of understanding on **richtlijnen thesis**, the root of the star's creation. The purpose and utility of the five pointed star could also be said to club be misunderstood by the Communists, not unlike the swastika adoption by the Nazis. [If the Nazi technology was as advanced in the flying saucer technology as is rumored then the swastika would not be far off.] For the time being I'm not doing full 2D (area) or 3D red stars until the bloody aspects dissipate -- oh, about a hundred years, considering China. These stars are fancies anyway.
Actually, Darwin started the whole mess with his 'strongest survive' evolution simplification, and it was the **richtlijnen** opportunism of Communists and Fascists who took in the reduction and used it literally. (There were alternatives available at essays Darwin's time but Mendel was pushed aside for **thesis**, the critical 15 years and at Mendel's rediscovery the industrial revolution was in full swing. Book review: The Monk in The Garden .)

What to look for. People bent on power will promote and support the **nora ephron a few words about breasts** following:
1. Nature is on our side.
Best represented by Dawkins' The Selfish Gene , the idea is that being loaded with money is natural (you guessed it, it's Gates' favorite). A virus is selfish, a gene is not. In the UK the **thesis vub** Oxford U nicely masks its ignorance with arrogance. In the **resume** US the Harvard U is **richtlijnen vub**, big on this kind of spin [they put out the best crap]. *Essays*. You will recall the dinosaurs and the dino eats dino times [I don't think they died out without a fight].

2. *Richtlijnen Thesis*. Running out of energy.
Usually about (peak) oil, this mentality replaced Running out of *on identity* food from the last century. This allows wars to go on, as it conjures up there is not enough for both of us. *Richtlijnen Thesis Vub*. This is but one example of reductionism. *Essay*. [If you don't see God, there are plenty of bosses to work under #150; here and on the other side.] The beauty of free energy is that it is really about smarts and without a large up front investment. Once you do a bit of reading, you will be LOL at the experts, but you'll also have to do the **thesis** free energy yourself. If you complain that the govt does not release free energy, you are not getting it.
3. Socialized medicine.
The mind job here is to convince you that you need the institutions of *paper on identity* state and selected private hospitals and clinics for you to stay healthy but there is an obligation to pay extra premiums.

It ends up that the healthier you are the more you pay and this becomes a tax on your health. Because you are smart and stay healthy by *thesis vub*, paying attention to your body's needs, you are pressured to pay for the ones who are not, and the power chasers are a sick lot. You may have to move to another state and/or become politically active (for example, AMA should not have a monopoly). You really begin to understand this when you start looking forward to stopping the payments of your premiums. You may find out **research paper on identity**, it is the **richtlijnen vub** best thing for actually being healthy. *Resume*. There are three components : understand fear, pick up specialized exercise, and keep up with alternate immunity discoveries (such as Dr. Jan Raa's) as well as the revival of Raymond Rife technology. Once you understand the **richtlijnen vub** fear component, talk openly about the **research paper** health alternatives should you meet an AMA doctor, for the tables might have turned.
4. Culture or religion-embedded values of guilt, fear, and intolerance.

Once embedded they can be invoked without explanation (prejudice will not be seen for what it is). This is usually about Bible and Koran waiving and could be difficult to deal with outside the US. In some cases the fear and/or weakness and/or ignorance justifies betrayal [needs to be watched, even self-watched]. Betrayal is also a component of power, and **richtlijnen vub** power has its own category (power is reversed in the virtual domain and there it is not based on **on laughter club**, specific might but on infinity). *Richtlijnen Vub*. In the Pythagorean and Buddhist traditions the friendship works well. I also like Ronald Reagan's attitude because he 'liked all and feared none.' You might get hurt but you will have the last word.
So you think you know your numbers and **research paper** might think it's okay to richtlijnen thesis reduce them to your liking. But if you construct the Great Pyramid with the golden numbers and use the **research paper on identity** shortest distance as the unit 1 , you will arrive at the pyramid's base as having the side length of 4 . The base of the Great Pyramid is then 4 times of *thesis* some unit of measure. So now the pyramid's base periphery (4+4+4+4) and base area (4x4) carry the same square number 16 . You see, if you reduce the numbers and **law assignments essays** think of the pyramid's base as having the **thesis vub** unit length of, say, two, the base periphery would have eight units of length but the base area would be but four (square) units. If you do not reduce the **adding gpa on** numbers you can think of the number 16 in the context of acceleration (unit of measure per time squared) and derive the unit of length that is most appropriate for this planet [yeah, it's a foot].

Rational numbers are commensurable numbers -- that is, they all have finite or repeating sub-unity part of *thesis vub* a number (mantissa) and all can be expressed as a ratio of two integers. Rational numbers can also be called the exact, finite, or absolute numbers because we can write them down and agree on their value. *Resume*. At times, rational numbers are called real numbers because all real things have a finite measure.
Rational numbers happen when we ratio two integers. All mainstream mathematicians define the rational number as the **thesis** ratio of any two integers. So, a mainstream math guy would say, Of course the rational number is a ratio of two integers -- it is **research on identity**, defined that way. *Richtlijnen*. Yet, you really do not want to be mainstream and acquire but an encyclopedia knowledge of the world. You do not want to think of somebody's definition as complete or adequate knowledge.

You know that a rational number is **paper**, a finite number (has a finite or repeating mantissa) and once it is finite it can be expressed as a fraction of two integers. As a smart person, moreover, you know that if another operation produces a naturally finite number then such operation also creates a rational number. The circumference of a circle is **richtlijnen**, a transcendental number. *Club*. Many of circle's round segments (arches) are transcendental numbers and their straight cord could be an richtlijnen thesis vub, irrational number -- and **essay on laughter club** both of *richtlijnen* these numbers have an infinite mantissa (infinite precision). The question now is: If you divide (ratio) some particular circular segment by its corresponding cord, will you get a finite (rational) number as a result?
Some Pythagoreans view the number two as a problem number because it divides the **on identity** unity. Pythagoreans discourage division of the unit 1 until you understand the context of each degree of freedom -- but in any case the number 2 is not the culprit. (The number 2 is in the denominator of the golden ratio and there it should stay as the number 2.) As you get familiar with this site the sub-unity will become applicable to atomic orbitals and hence the number 1 is the Great Divide between the macro-cosmic and micro-atomic. [My guess is that macro concepts are taught before the micro in the Pythagorean School.]
Tetractys of *thesis* Pythagoras deals with the organization of matter, among other things.

What makes you a Pythagorean? Short of visiting the Pythagorean page, you are interested in the actual construction of the visible universe. As a Pythagorean you want to know why some stars are constructible exactly and muse at the people who draw stars without regard to their actualization. Drawing stars just for **club**, fun is okay but to a Pythagorean that's in an entertainment category. The.
compilations about stars are trivia, which quickly become distracting as well. Working the five pointed star is a wonderful start, for this star is geometrically, that is **thesis vub**, exactly, constructible. Constructing the real universe is, moreover, the **body theatre death** greatest show there is.

Construction and deconstruction of atoms are similar endeavors -- and you have no need for a hammer to construct or deconstruct something. The forces therein can add up in controlled fashion, too. There are dozens of philosophers and gurus talking about the omniscient nonlocal instant infinity of the **thesis vub** conscious universe, but to a Pythagorean this is but one half of the show : You still have to put all that knowledge to work. Yes, we have pictures. The upside down star has no negative meaning in the micro domain. There are in fact several stars nested inside the larger stars because there are many orbit jump opportunities with each pair of *amusement park essays* orbitals.

Yes again, ALL triangles are golden.
Oftentimes we think of star patterns only when tiling in 2D or building the Platonic solids (in 3D). But the **thesis vub** patterns we encounter in the micro are usually made with overlapping stars and that makes nifty art shapes as well. The overlap comes from the **law assignments essays** inclusiveness of waves.
On July 17, 1991 at vub Barbury Castle there appeared a crop circle named the **nora ephron a few words breasts** Tetrahedron (a triangular pyramid). *Richtlijnen Thesis*. For its 20th anniversary we have a summary-update.
Here is a poster for **adding resume**, a Graphics show I had in Prague (where I teach now) in February 2013.
Large-print format is **thesis vub**, becoming affordable. With a careful equipment selection, one can avail to a high quality original poster that is not only less than the price of a reproduction, but is good for your health as well.
Just about ready (second picture).
Consider the existence of the even and odd symmetries as the point of departure between the Pythagorean and Aristotelian physics.

Pythagoreans continue basing new concepts on numbers and then the even aka twofold symmetry issues from and relates to the number two (and the feminine). Aristotle refers to the Pythagoreans and flatly claims in Metaphysics that 'two' and 'twofold' are not the same and **essays** that 'twofold does not subsist in the two.' (Of course) the two and twofold are not the same but the number two spawns the even symmetry as two-points-make-axis construct and then the number two is not just a counting number.
If Aristotle rejects the Pythagorean 'number two is behind even symmetry,' does he propose something better or different? It does not seem so, and this could be a nice example of *thesis vub* ancient Greek debunking. *On Laughter*. Aristotle does not like it, and that's okay, but without offering his own reasons for the existence of symmetries he will not be able to advance it. Sure enough, we don't hear from Aristotle on **vub**, symmetries.
Some star constructions speak of *on laughter club* fixed length sticks, which at first glance can construct any size polygons. Here is **thesis vub**, where the executability of angles comes up. In space, the **a few words** irrational angle is constructible only approximately and only some angles will be actualized #150; think snowflake formation.

Also, we can calculate the points of a polygon along a circle but using sticks that have finite (rational) and equal lengths for the cords will not always fit in such points. In fact, a not-so-difficult case can be made that geometry takes precedence (has priority) over arithmetic. [If you are a scientist, you may think of Emmy Noether who ignored the nature's beauty of snowflakes and made simplifying assumptions about space that proved the **vub** 'ignorance is bliss' postulate #150; for in her world everything is reduced and **essays** snowflakes and **thesis** crystals don't exist.]
You can calculate the area of any polygon by *nora words about*, taking the **thesis** area of the triangle and multiplying by the number of sides. When working the area of *amusement park* a circle or a polygon, the center point is (becomes) excluded . (If you are metaphysically inclined, think Isis looking for all parts.) In your Pythagorean mind, you need to thesis link the area to its physics application. For example, a physical property that is **essays**, proportional to radius squared is then also proportional to the area, which gives merit to area calculations. This is bigger than it seems. *Richtlijnen*. You are not just sweating your teacher's assignments -- you are actually working the physics entities if you know what they are.
This one comes from Yosifusa Hirano of 19th Century Japan. It is elegant and also constructs the pentagon or pentacle on radius 2.
All pentagram angles are a rithmetically divisible by nine.

So, what's the big deal if the **gpa on** number 360 (degrees in a circle) is **vub**, no big deal? If you line up all angles from the pentagram : 36, 72, 108, 144, etc. and **essays** sum their individual digits you will always get 9. That may seem like magic, but once you appreciate that the number 360 is arbitrary, you don't need to richtlijnen thesis ooh and ahh about it. If the number of degrees in a circle were 320 or 260 or 364 the summing magic would not happen for **nora ephron essay a few words about**, 9. The circumference of a circle is 2Pi and **thesis vub** putting in a number to stand for degrees is purely a practical consideration. In the case of 360, this number is 4x9x10 and now, because the angles of a pentagram are in tenths of *amusement essays* a circle, the **richtlijnen** number that is left is a multiple of 9 (and 4) and so it will be always divisible by 9 (or 4). All numbers divisible by 9 have their digits sum up to 9 (modulo 9 #151; thank you, Gauss ). So, always work with fractions of a circle (or fractions of 2Pi) even if the **body essays theatre** numerical sub-unity pushes your right brain into infinities. *Thesis*. There is plenty of real magic left in this subject, particularly if you get into the squaring of a circle.

We have a collection of *amusement essays* cool and hot designs inspired by the five-point star. View select designs -- or visit our store at Zazzle ( . com/Mike_Geo) and see how well you could look in a tee, hoodie, long sleeve shirt, or a polo. If you have new ideas you want to explore designs from the constructs of nature. All our designs come from nature and center on the golden proportion.
Design on right is called the Adventure of *richtlijnen* The Red Sun.

A pentagon and **gpa on resume** the Great Pyramid are related, but it hadn't been easy to show both of them relating through the golden proportion. I construct them together using the new Golden Eye method in the Quantum Pythagoreans book and now the construction is available in color for your shirt or Tshirt as well -- in the Golden Eye design.
The golden proportion is between the pyramid side and the half-base. The Great Pyramid is shown in a vertical cut through the **thesis vub** mid-face. *Memory Body*. Much detail is on the golden numbers page.
The five pointed stars attract energies on account of the **richtlijnen thesis vub** golden proportions. Because under rotation the five fold symmetry can be either harmonious or disharmonious, you want to know which is which (ccw is harmonious on a pentagram, cw is harmonious on **amusement park**, a pentagon) because you really cannot hide under a rock and hope for the best. Some people rely on intuition and some want to understand things a bit first.

Either way, I wish this site and the book will do it for you.
Two pentagons make a decagon, a regular ten pointed star.
A regular pentagon made with the Hirano method can be used to easily make a regular decagon #151; an exact ten-point star. *Thesis Vub*. A pentagon that is **nora ephron essay**, made by the exact division of *richtlijnen* a single circle can be duplicated 180 degrees out-of-phase (upside down) and decagon results from *paper on identity*, two pentagons. One pentagon is thus rotated about the **richtlijnen thesis** center of the **park essays** circle or, if you prefer, rotated/flipped about the horizontal axis.
However, a regular ten pointed star that is a regular decagon is not a hyperstar. (Hyperstar is discussed in *thesis* the right column.) While both stars are created from two regular five pointed stars, a decagon is always convex.

A hyperstar has some straight segments spanning three points. A decagon has its points on a single circle. A hyperstar has 8 of its 10 points on two identical circles separated by the golden ratio parameters.
[I think the mathematical discoveries of construction ratios is what Plato refers to as 'Logistics,' which is thought to be a lost Pythagorean knowledge. *Essays*. In the **richtlijnen** case of *nora ephron a few words about* a pentagon Diameter priority the ratio is with square numbers (1:4) because we go from *richtlijnen*, 1D (unit length) to 2D (circle). The same ratio of 1:4 holds for the pyramidal construction because one unit of length ends up as four area units of a pyramid base. For a pentagon point-to-point Length priority, however, the ratio is 1:2 because one length becomes another length (1D to 1D) but the construction now must include rotation . In general, there is a rotational aspect in the Pythagorean Theorem even though the **essay** arithmetic of the Theorem does not capture it (it uses squares). *Thesis*. Logically, any line (any 1D distance) inherently contains a direction and when staying in 1D a change in direction amounts to rotation. Squares (area, 2D) do not contain a static direction but they have something else.]
Every time you double something #150; think octave.

Every time you halve something #150; think node (or fit) for standing waves. Every time you rotate by 45 degrees #150; think transformation. Every time you rotate by a right angle #150; think.. The funny thing is this works for Tai Chi when your body, your arms, and **park essays** your legs are doing the movements. *Thesis Vub*. Geometry and **gpa on resume** movement is about your health too.
Harmonious ten pointed star.
The star below, if drawn counterclockwise, is classified as a (10+ 7 )/10 star using my method that is **thesis vub**, (x+y)/x in *body theatre death* general y is **thesis vub**, between 1 and x #151; that is, xy=1 . The decagram star looks nice #151; it is unicursal, is regular during construction (advances by the same angle), has parallel sides and is harmonious.

This star skips every six points and is the only harmonious ten pointed star in *amusement* the macro. (Decagon and **richtlijnen thesis vub** all other ten-point stars are not harmonious, cw or ccw.) The Pythagorean style rationing (really proportioning) method (x+y)/x as well as the corresponding musical harmony or disharmony is explained in *club* the book, and you'll know why the proportioning approach presented here is much more useful than what the mainstream puts out. You noted x and **richtlijnen** y are integers but if x and **amusement essays** y are the golden numbers then (x+y) : x is the golden proportion #151; and enter both the micro and the macro. *Thesis Vub*. (Rationing is not commutative because A/B is not B/A. Proportioning, however, is commutative because A : B is the same as B : A, and playing two musical notes has the **law assignments essays** same effect whether you analyze at it as A : B or B : A. Sometimes I think mainstream math is pathetic, for ignoring waves is the norm.)
There exists symmetry about one point called the point symmetry (or odd or radial or rotational symmetry) [masculine]. There also exists symmetry about two points called the even symmetry (or axial or twofold or mirror line symmetry) [feminine] #151; the two points making an richtlijnen, axis by *breasts*, which the original image rotates. These two kinds of symmetries are all-pervasive in atomic construction where they are called the **thesis** odd and even wavefunctions. Yes, everything is coming up numbers. Now, how would you marry these two symmetries?

You might have noticed that in the five-fold division of a circle the three points made by *adding*, a compass' pin are at the corners of a right angle triangle having sides 1 and 2 . *Richtlijnen Thesis*. (A pin of a compass centers the radial symmetry [masculine].) It is no coincidence that the **essay on laughter** Great Pyramid's Grand Gallery has the **richtlijnen** vertical height (rise) of 1 and **nora ephron essay a few breasts** the horizontal length of 2 while the Trough is the hypotenuse spanning the distance of SQRT (5) . (This also establishes the **richtlijnen vub** unit length 1 of this pyramid.)
Is it a coincidence that to define Pi we need distances 1 and 2 ?
Is it a coincidence that to construct the **amusement** golden numbers we start with a right angle triangle with sides 1 and 2 ?
There is more to 5.
It is very easy to thesis get excited about the **amusement park** number 5 and begin to associate each of the five points with other things. *Thesis*. This is a Pythagorean site and we love the number five but Pythagoreans also know that using numbers for counting is introductory to the power of numbers while correspondences are about the elemental #151; that is differentiating, power of *essay club* numbers. The five discrete elements in Wicca and Tao are fine, yet the visual-geometric imagery based on the Penta.
is about the infinity (irrationality) of the golden proportions stemming from the **vub** square root of *park* five . *Richtlijnen Vub*. With the golden numbers you construct many shapes that extend the Penta.
beyond counting. The images are also more than pretty pictures, for the waves in space readily interact with such shapes in a computing relationship and things happen. You do not need to get esoteric to appreciate that energies have preferences for geometric shapes and the golden proportions have a unique predisposition to the operation of the reciprocal . *Nora A Few Words Breasts*. (Yes, energies make things grow but also think about the **thesis vub** nature's way of actually capturing the waves' energies.) So it is nice to recognize the golden shapes around you even though neither the star or the number five jump out at you.

The meaning could be shifted by another application but now it is not hidden. [There are also large corrupting influences in place just to keep you astray.] What if the **body theatre** Queen's Chamber in the Great Pyramid has its spatial distances in the golden proportion? What if the spiral on the Eye of Horus were made through the golden rectangle or a golden triangle? How can you visualize the golden ratio in financial terms?
Throughout the Hyperflight site I like to make fun of mainstream science. These folks lower our understanding and appreciation of nature and **richtlijnen** their favorite first step is that 'this or that cannot be done or found out.' The best modern example is Einstein and I don't know of any of his concepts that are correct: This includes the special and general relativity theories (stemming from his inability to determine absolute motion/rest); photonic work function (a photon puts no pressure on **on laughter club**, a mirror); Brownian motion (molecules vibrate in place); and **thesis vub** energy-matter mechanics (not reversible, i.e., nova or supernova). *Park*. Errors of omission and commission are also applied to corrupt the reality around us.

The basic difficulty is that science popularizers use the right math but apply it to wrong concepts. It may take a while to get to the bottom of this and **thesis vub** what really helps is **park**, that equations cannot make wrong concepts right, and therefore are suspect.
On this page I said that 'up' and 'down' cannot be distinguished in the solar system under odd symmetry alone. *Richtlijnen*. Everything works and continues to memory essays theatre grow, evolve, and can also be created whole in a particular context. *Richtlijnen Thesis*. It is then the context that needs to be understood in addition to any some such conclusion. The 'up' and 'down' manner of speaking is relevant when the context has a line : things above the line are 'up' (above) and below the line are 'down' (below).

However, orbits and **law assignments essays** orbitals and spin in *thesis vub* general have a point as its construct of rotational/spinning existence and it is **law assignments**, then appropriate to say that when dealing with point symmetry there is no fixed 'up' or 'down' because there intrinsically is no (fixed) line. *Richtlijnen Thesis*. The point is that if you understand the **on laughter** context you will understand whether someone's pronouncements are true, not true, or corruptive. For example, ignoring 0D (a point) as the fourth dimension of freedom -- which provides a movement construct just as 1D, 2D, and 3D do -- is corruptive because it does not recognize the spin/orbit that accounts for 99% of the moving energy found in the universe. There are several ways of *thesis* getting to essay on laughter the truth, too. Geometry is one. Tarot works nicely and in *richtlijnen* this case it's The Wheel of *memory essays* Fortune card.

Tarot has four suits, which stand for **thesis vub**, .. (your brainwork). You will then be in position to either speak out and/or just do what you know is **essay on laughter**, better : Free energy, Martial arts, spiritual medicine, telepathy/RV, superluminal travel, atom/matter creation -- all, not coincidentally, based on ether scientists deny. Speaking out means that you have enough info based on merit and then your statements become less political. For example, I'd get a Tarot card deck without the Hebrew letters, for these lack symmetries and could be disruptive. (If you know the Hebrew letters were added to Tarot later on, you'll also know it is about corruption.) As you learn how things really work the misconceptions will release and you become healthier.
After reading a book on the history of the Chinese philosophy that weaves through the Confucian, Taoist, and Buddhist pursuits over thesis vub 2300 years there, it seems the Chinese never got to the understanding, and then the differentiation, of the symmetries.

Yet I would not relax too much after this. There are the philosophical and religious versions of *nora essay a few* Taoism and **richtlijnen thesis vub** if you stay with the academia's version of philosophy you'll learn next to nothing. Once you get to the religious side you will read a lot about circles and spirits and demons, about keeping centered (weighed) in a point and having light crystallized -- but all this is pure alchemy and it takes some dedication for **nora breasts**, the ideas to work their way through (just as you would do with the ancient Egyptians). While the Chinese did not push the three philosophies/religions into **thesis vub**, the objective realm we call science, the **research paper** Chinese pursuit in the improvement of the individual's mind-body yielded Tai Chi with most significant implications -- and leaving a formidable gap for the West. Wang Fuzhi (b. 1619) gets very close, giving Chi (Qi, Ether) the female-male aspects of Yin-Yang (ancient Egyptian Tefnut-Shu) and then nicely extends this to thesis vub coexisting energy-matter duality along with a dynamic balance of the two. Wang Fuzhi is describing a free electron all right but then its detection and use happens in a body (yes, yours) rather than in an external and objective instrument. (Damn the self-serving Emperor/one-party systems and invest in yourself, literally?) Wang Fuzhi, or anyone after him, does not advance Li (order/construct/distance/1D) to geometry or symmetries, and this also means the Pythagorean tradition did not make it to China (until recently perhaps). *Paper On Identity*. We can then also say that the Taoist five pointed star of the elements is indigenous to China (could've been discovered in more than one place) and testifies to the universal power and utility of the five fold division of a circle. The Chinese elements correspond roughly to those of *thesis vub* Wicca except that 'spirit' is taken as 'wood.' This seems strange but think of wood as the circles of tree rings, too. This also gives you an law assignments, idea how hidden Chinese alchemy is. *Richtlijnen*. (Note the prominent spiritual link to the trees in the Druid tradition and a very explicit tree related experience of *nora ephron a few about breasts* Joan of Arc.) The Taoist movement starts with Lao-tzu's Te-Tao Ching of 500 BCE (or so) and Te translates as Virtue. I am happy to have named the largest chapter in the Quantum Pythagoreans book the Virtual Domain (and before reading Te-Tao).

The virtual domain is **thesis**, about infinities and there is much to adding resume explore there -- yes, this is an understatement. (One can also destabilize in John Nash fashion. If you don't figure out you are among infinities while using real/rational methods, you may stay there forever.) If I were to talk in Lao-tzu's puzzling way, the virtual domain Te holds nothing because it has everything (and now you'd have to figure out the virtual domain Te has everything in the form of knowledge). At times Te translates as Power (and knowledge is **vub**, a close relative of power). *Research Paper On Identity*. Lao-tzu described Tao in the most general way. It was only *richtlijnen* later that the Tao symbol arose from that and along with the religious side of Taoism. But of course, the Tao symbol is **nora ephron a few**, but the Chinese version of what the infinite Tao is or could be used for, including the label of *richtlijnen thesis* 'Tao.'
The virtual domain deals with knowledge that is linked by associations.

The Western alchemy's condensed virtual language could speak of the philosopher/sorcerer entering the stone only to discover there is no stone. Bewildered, the **law assignments essays** philosopher breaks out of the stone and finds the stone the same as before. He cannot break into the stone and yet he does not have to break up the **richtlijnen thesis** the stone to reenter it. *Adding Resume*. The philosopher's stone can be had -- but not physically. Yikes!
Here is **richtlijnen thesis**, s'more on stability via organization.

So you think you know your numbers metaphysically and feel comfy about the masculine-feminine stuff. You might be dividing by 2 and think it feminine. Not so. Real cutting is masculine : it makes two halves of an apple, severs an interconnection of a relationship, or spatially reduces a spread out electron (QM). However, when you observe a biological cell division, don't rush to call it masculine, for it is feminine. You'll have to get into symmetries to understand this.

Meanwhile, don't make the silly mistake of equating masculine with a man and feminine with a woman -- unless you want to give up on one half of your brain. Oh, and think about The One. Analytically attacking all three major pyramids at Giza as one layout can earn you a label or two, but on this site Jiri starts with a square and then looks for the golden proportion #150; and gets very, very close to the actual measurements. Ready to essays bury the Pharaohs someplace else? Some basic geometry. From a square angle to a square. There does not appear much we can do with a square. A square is pretty, has a lot of symmetries, but that's about it. But as we go on, things are going to get interesting once we start to richtlijnen make cubes.

Also, as a plain square, two circles can be fitted and defined by a square: an outer circle and an inner circle. The illustration on left is taken from our ether page and it actually results in geometrically determining the speed of light.
A square and a circle have been engaged from before Pythagoras (Thales) and there are several pages on this site (here and **adding gpa on resume** there and here too) on circle squaring.
Pythagoreans love square numbers. In the present day vernacular, moving energy is **thesis vub**, proportional to velocity square d. Any square can be made into any number of rectangles and any rectangle can be made into an exactly same-area square via the geometric mean. Geometric mean works with all distances, including irrational distances (but you need rotation). And so any and all velocities resulting from, say, gravitational acceleration or collisions or explosions, have corresponding and exact energy values.

Any square (any amount of energy) can be divided into as many squares as you want #151; and so the energy of one moving object is conserved exactly even if the **nora a few** object is broken up into many other objects.
Here is a simple yet powerful construction that.
1) Divides any distance exactly in half;
2) Erects the perfect right and square angle (making the Cartesian Coordinates); and.
3) Makes a true square using any circle centered at O (at the intercept of horizontal and vertical axes that are the **thesis** coordinates). A square is also a four pointed star.
Only straightedge and compass are needed. (Straightedge is an unmarked ruler.)
Both arcs (arches) have the same radius.
Distance AB can be either rational or irrational, for there are no limitations on spatial distance between two (zero-dimensional) points A and B. Drawing a line between two points is about direction (1D) and yields a perfect line, too. If you want to know the minimum separation between points before a line could become the real line, take a look at Absolute Minimum Length (it's about the infinitesimal).
If distance AB is irrational, should it be dashed?

If so, why?
You will note that all geometric constructions start with the creation of the Cartesian Coordinates. Once you have them, you can make any square using a compass (a circle) and then make any star from the perfect star family. A square, then, is **adding resume**, inherent in all star constructions.
A square is feminine and a circle is masculine. *Thesis Vub*. Some people get into spirituality and claim a circle is feminine because it is rounded. That is how you can tell a beginner. Symmetries are the key here because they have very high priority -- on par with energy conservation.

Ancient Egyptians, Native Americans, and **ephron a few breasts** Chinese have no problem here. Pythagoreans and Plato are technically fine because of symmetrical 3D solids. Aristotle would not get into symmetries at all (and his historical contribution ends [should've stayed and die in *thesis* Baghdad]). *Research Paper On Identity*. The Western applications of symmetries are generally weak, although, the Western alchemy is **thesis**, okay and at times superior (3 vs. 4).
Three pointed star.
Construct the **amusement park essays** perfect triangle on **richtlijnen**, a circle and another triangle on a semicircle #150; in three steps.
Triangle as a logical and **law assignments essays** mathematical construct.
Because three-pointed and six-pointed stars are geometrically perfect they can be used, circled, as a symbol for 3 or 6 wavelengths wrapping around the nucleus. *Richtlijnen Thesis Vub*. However, a hexagon and hexagram reduce into a triangle under modulo math for harmonious ratios and do not manifest in *a few words about breasts* orbits (macro) #151; that is, showing a six-pointed star with two circles does not reflect nature.
A hexagon is also prominent in free energy work.

Hexagon is full of different symmetries and, for better or for **richtlijnen vub**, worse, enables rapid transformations or projections. A six sided star of hexagon could be of some interest regarding energy accumulation in the micro and we included it in the numerology section on the Pythagorean page.
Without a circle, a triangle symbolizes 3-state systemic (complete and **essay club** never-ending) systems, each state being in one corner. Such three pointed arrangement has no metric as it is a logical, say clockwise, process. (Some systemic processes call for quaternaries #151; think ancient Egyptians.) For Pythagoreans a triangle provides bounds for the ten dots of Tetractys (a triangular numeral 10), which also becomes one facet of a tetrahedron (projection from the apex [or from your eye]). The right angle triangle does have metric of the Pythagorean Theorem, which relates 1D to 2D via (ir)rational numbers (but does not solve for transcendentals).
There is a very special place for the golden triangles. Two kinds of *vub* triangles apply here, depending on whether the **paper** shorter or longer distance is used for the triangle's base.

Golden triangles facilitate a perfect relationship between particular two circle's circumferences and **richtlijnen vub** a straight distance. Yes, this is the fundamental reason for the existence of particular atomic orbitals, which is driven by the exchange in the electron's 2D and photon's 1D energy . This is not strictly about the squaring of a circle but it is close (it's about the difference in 2D energies).
Differentiate by *adding gpa on resume*, 3.
Finally, there is an aspect to the number 3 as the fundamental qualitative differentiator of nature. We are mostly familiar with the dualities such as the **richtlijnen thesis vub** real-virtual (Yang-Yin) or odd-even or ordered-creative but there is **body essays theatre death**, also a lesser known differentiator by three. Yes, we say animal, mineral, vegetable and think it special, but here we are very fundamental. Pre-atomic, I'd say.

So much so the **thesis vub** crop circles are worth studying just for **research**, that. [I would not go inside a crop circle for more than a few seconds when the circle is less than a day old #151; it is about the 3D energies.] Alchemy's sulphur, salt, and mercury gets into **richtlijnen thesis vub**, that as well but without geometry it's an arduous road. The Quantum Pythagoreans book explains what is at memory death each corner of the Tetractys and that's what it's about.
When you see a triangle with some symbol in the center (a dot, an vub, eye, dragon), take such symbol into 3D of the apex of a tetrahedron to see if it means something to adding gpa on you.
Instructions: Draw horizontal and vertical lines. The intersect is the origin O.

Draw a semicircle of radius r around O . *Richtlijnen*. This makes point V.
Draw a circle around V of radius r.
Now that we divided a circle into exact thirds, you can make a three pointed (Mercedes) star or a three sided star of a perfect triangle. In the illustration the larger triangle divides the **resume** circle with three exact cords of length c for a perfect three pointed star.
The smaller (red) triangle divides the **thesis vub** circle with six exact cords of length r resulting in a perfect hexagon or hexagram.
You can verify (using the Pythagorean Theorem) that the relation between the **nora a few about breasts** cord c and **thesis** cord (radius) r is:
What physical entity is proportional to r 2 ? If you know what that is, consider that the square of the cord c is three times that.

A puzzle of a bad souffle: Given a square, construct a new square that is exactly one third of the original square.
You can be fairly certain that the person will try to partition the square in some way but the **theatre** solution is to erect a triangle on the square's side and then obtain the radius for the circle that covers the triangle. Radius r is the side of the new square. [In our case the bad souffle does not cave in *richtlijnen thesis vub* but runs over nora ephron words breasts the rim.]
It is not possible to reverse engineer a souffle without stepping back and understanding the relationships between the ingredients and their proportions #150; as well as the irreversible nature of the baking process.
Can you apply the construction of the geometric mean in *richtlijnen thesis vub* the solution of this puzzle? Could you use the geometric mean to generalize this puzzle for all possible ratios of square areas? If so, you would then be able to divide a square into any number of squares, including squares with irrational sides.

The geometric mean equates the **amusement essays** perimeter (or area) of any rectangle to the side (or area) of a particular square.
Could squares with irrational sides be included in the general division of a square into any and all other squares? If so, does it mean that geometry does one up on arithmetic once again because arithmetic cannot give you the exact irrational number for the square's side?
Finally, if energy of a moving body is proportional to its velocity square(d) , can you divide such energy square into as many smaller square energy components as you wish? (Via a collision, gravitational attraction, or some other action-at-distance?)
A six sided star, a hexagon, is prominent in virus structures. Hexagons are partioned into a six-triangle grid, which serves -- through a geometric relation -- to richtlijnen thesis identify almost all viruses.

This is a complex topic. For example, a virus' hexagon is rendered benign with a pentagon [my own thing]. The overall structure in 90+% of viruses is icosahedron . Although labeled 'an esthetically most pleasing shape' by some -- with 5-fold, 3-fold, and 2-fold symmetries -- all mainstream scientists ignore the **body essays death** morphing nature of the virus first brought forth by Rife (bio) [virus approaches under a friendly flag and morphs]. Because the current work on viruses discloses but the **thesis vub** stained (i.e. dead) viruses, the mainstream is still way behind Rife. If you understand the corrupting mechanisms in the present day medicine, you will know why you do not have to join a walk for or against this or that disease. You don't have to essay on laughter follow, or agree with, generally published explanations but spend your money and time your way -- and a better way at that.

There are several recent breakthroughs in virus' geometric construction. The geometric steps in virus' formation are : diagonal projection of a cube resulting in a hexagon; slicing-and-projecting a cube grid resulting in *richtlijnen thesis* a hexagram (aka the Star of David); and rotating-and-zooming (as shown above, [which is the final projection onto *law assignments*, the material plane]). I see some of *thesis* these elements in the crop circles and, short of taking sides, I'd like the virus construction viewpoint represented in crop circle analysis. We are dealing with a very advanced technology but it is very advanced only because the mainstream science coming from the universities is **about breasts**, primitive and **thesis** corrupt.
In practical terms the twelve pointed construction is about the design of a clock's face. In astrology the twelve Signs of the Zodiac is **park**, about the twelve sided division of the Solar ecliptic. *Richtlijnen Thesis*. There is an even more interesting side : There are twelve computable states along the **research paper on identity** periphery at the third level of the Great (Golden) Pyramid.

In the infinite superposition of the virtual variables (aka wavefunctions), there are geometrically enabled states inside the pyramid that allow a computable state to form. Yes, infinities can be worked and the Quantum Pythagoreans book gets into that and at all levels of the pyramid.
Our construction for the twelve fold division of a circle also divides a circle into eight exact segments, or angles, because the 45 degree diag onals are available for free from our twelve point construction if you make full circles (and don't stop at the intersects with the central circle). *Richtlijnen Vub*. This is also true the other way: When constructing the eight point division that is a regular octagon, the twelve fold division happens as well if the central circle is drawn in *law assignments* full (and you don't just mark the intersects with the cardinals). *Richtlijnen*. So here you have the combined 8 12 point star construction. *Amusement Essays*. After a short Internet search I did not find an 8 12 point star common construction . I found one logical assembly having the Chinese Zodiac on the outside circle and eight binary Paqua states on **richtlijnen vub**, the inside circle. (This tells me divination is intended but, because of our inherent construction feature, I'd turn it around the **adding gpa on** other way : 12 sides on the inside circle and **richtlijnen thesis** 8 points on the outside circle. This is counter-intuitive but there could be [is] a form of Tai Chi in this.)
The common construction of the eight and 12 pointed stars starts with the **research** combined two and **richtlijnen thesis** three pointed stars.

As you double the count the ratio stays the same : 3 to 2. (As you double the points you go up by *law assignments*, an octave.) This is a musical ratio and a harmonious one at that. What planets subscribe to richtlijnen this ratio? It is not Venus-Earth but it is on the Venus page.
The eight pointed star is **essays**, full of symbolism associated with Venus and the transformations via the **thesis vub** diagonals. *Amusement Essays*. The ccw octagon is harmonious and made by Earth-Mars interplay, too. *Richtlijnen Vub*. So enjoy the eight-point star construction here via the cardinal and semi-cardinal directions but the **paper** Venus page has a lot more on the eight fold division of *richtlijnen thesis vub* a circle, including the Hunab Ku symbol.
These watch face designs are inspired by the Mesoamerican Hunab Ku symbol.
Instructions for drawing a 12-pointed/12-sided star:
1. Draw a horizontal line and erect the vertical line.

The intersect is the origin O.
2. Draw a full circle of *essay club* radius R around O . This will be the clock face.
3. At each of the horizontal and vertical intercepts draw additional circles of the same radius R.
4. The intercepts of the central circle with the cardinals and **vub** with the other circles yield the twelve points exactly distanced around the **essay on laughter club** central circle.
Can you see how you could make a 24 point star using the diagonals? Almost every month we offer quick topics of general interest. In May 2011 a single construction shows how to thesis vub make both the 24-point and 16-point stars in just one construction.
Perfect star families.

It is **research paper on identity**, easy to draw stars using geometry's tools, a straightedge and compass. By now we want to richtlijnen thesis vub make stars geometrically, not just for perfection, but also because only the perfect stars manifest in nature. A circle can be divided exactly into 2 , 3 , 5, 15 , and 17 equal segments, technically called constructible polygons. (Some exclude the 2-segment division because it yields but a virtual line of *on laughter club* a circle's diameter #151; but I include it.) You may call this the 'fundamental' or 'primary' or direct sequence of perfect stars. Since any and all segments can be also exactly (evenly) divided by 2, you can find all stars that have their points exactly spatially distanced by geometric means. You can also say that the **richtlijnen thesis vub** doubling expansion forms a perfect star family.
For example, you can make an eight point star or a 64 point star from a two point star through simple halving of distances. From a three point star (above) you can make the exact hexagon and from there the twelve point star of the Zodiac or do a layout of a twenty four point star for Feng Shui.
Starting with a 2 point star #151; the **amusement** only direct even star #151; you can construct 4, 8, 16, etc. stars you could also label the 'evenly even' sequence of *richtlijnen thesis vub* stars. This is the original Pythagoreans' terminology, which presently would be called the 'binary' sequence of stars.

From the 3 point star you can continue to theatre death halve each side to make the 6, 12, 24, etc. point stars. *Richtlijnen Vub*. From the **law assignments essays** five-point star you can make the 10, 20, or 40 point stars.
Every perfect star with the even number of *thesis vub* points will have symmetry about an axis and about a point. If you think there is no such thing as a two point star, it is on the Venus page and **amusement park essays** it is formed by the combined Neptune-Pluto 3:2 orbit.
The stars that are left out from direct and doubling constructions cannot be constructed exactly. For example, you cannot make a nine point star directly #151; or indirectly from a three point star. The seven, eleven, and thirteen pointed stars are also not constructible.
Numbers that divide a circle exactly could have a name of their own. A good fit is 'circumpositional,' for these numbers compose in a circle exactly and will be [are] prominent in atomic constructions.

Carl Gauss recently added the 17 sided polygon as the perfect star. The 15 sided polygon is in *vub* Euclid 's Elements , Book 4, Proposition 16, and is made by a combo of a three and a five pointed star (a 5-point star is evenly rotated three times around the **park essays** circle).
One interesting property of the perfect star families is that they do not intersect directly. A sequence growing from each of the **richtlijnen** direct perfect star number does not match (overlap) with another sequence. That is,
from 2 we get 4, 8, 16, 32, 64, 128, 256, 512, 1024 , 2048, 4096, 8192, 16384, 32768, etc.
from 3 we get 6, 12 , 24 , 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576..
from 5 we get 10 , 20, 40, 80 , 160, 320 , 640, 1280, 2560, 5120, 10240, 20480..
from 15 we get 30, 60 , 120, 240, 480, 960, 1920 , 3840, 7680, 15360, 30720..
from 17 we get 34, 68, 136, 272, 544, 1088, 2176, 4352, 8704, 17408, 34816..

Each member of the perfect all-star family has but one origin. Once a number becomes even it stays even. *Research*. 3, 5, 15, and 17 make the only exact odd stars.
A circle is a zero pointed star having an infinite number of points. On a circle there are no inbound-outbound changes and, therefore, no points. Topologically, however, a circle is composed of infinitely many geometric points. This is a technical play on words. However, a single geometric point, a 0D point, has an infinity built within it [yeah, takes work].
360 does not divide a circle exactly.

260 does not divide a circle exactly (Mayan Tzoltek calendar). The end of the Tzoltek calendar is not (cannot be) synchronized with a rotational parameter such as the precession. *Thesis Vub*. It is **adding gpa on**, conceivable the Mayans had difficulties reconciling the rotational parameters (based on transcendental numbers) with some linear time-measuring parameters. The numbers' unexact nature would lead to richtlijnen thesis disaster conclusions. *Resume*. Well, yes, it could have been their own square-a-circle problem.

320 does divide a circle exactly and the 1/320 (reciprocal) is **thesis**, called ro by the ancient Egyptians.
While a circle can be divided exactly by hours (24) or minutes (60), a circle cannot be divided by hours and minutes (24x60=1440).
60 does divide a circle exactly and the sexagesimal (60-base) system is **on identity**, first used by the Sumerians (2000+ BCE). Although all mainstream math books claim we use 60 minutes and **thesis vub** 60 seconds as a result of Sumerian and Babylonian cultures, none of *gpa on* these math references mention that while 60 does divide a circle exactly, a circle cannot be divided exactly by minutes and seconds (by 3600). But of course, mainstream math is cluless on what the exact geometric circle division brings to the table.
While a circle is divisible by 10 exactly, a circle is not divisible exactly by *richtlijnen vub*, a hundred or a thousand or any higher decimal multiple. The decimal fraction format aka the decimal fraction notation is **amusement**, not suitable for the circular geometry beyond the first decimal point.
Is it strange the Mayans #151; while having the positional notation of base 20 #151; had no sub-unity base-20 fractions? Perhaps not. *Richtlijnen Vub*. Just as in the decimal and sexagesimal systems, the base 20 (vigesimal) system is useless past the first vigesimal point in circular geometry.

One star inside another star.
Among the applications are spatial designs that combine perfect stars. In watch design, for **ephron essay**, example, the circle being divided by twelve looks fine and is harmonious. *Richtlijnen Thesis*. In addition, it is harmonious to overlay the 12 point layout with triangular, square, or pentagonal designs. You would not want to put a seven point star with a triangle together in the same (concentric) circle, for example, unless you want to invoke disharmony. Six gets tricky because it is disharmonious with larger numbers but is **amusement park essays**, harmonious with five, making a pentagon (not a pentacle). There is also a disharmonious ccw pentagon and that one does not include six.
When using but a single star you choose one from the **richtlijnen** perfect star families. When combining stars, however, you also must deal with harmony. A doubled star is always harmonious with its parent star -- they differ by an octave, but not all star combinations are harmonious.

We are talking about harmony in *research paper on identity* point symmetry, which is **richtlijnen thesis**, applicable to both the micro and the macro. See the book.
If a musical tone x is harmonious with tone y and y is **body theatre death**, harmonious with z , is z harmonious with x ? Not always. The book explains harmony's geometric foundation and **richtlijnen thesis vub** then the star drawings bring harmony into the visual range. Quantum Pythagoreans provides the formula for harmonious musical notes and you will also know why some stars just do not feel right.
Harmony is not just extended to the macro. Harmony is fundamental to both the micro and macro constructions and, therefore, to stability in general.
Thanks to Paganism, a five-pointed pentacle star is presently classified as harmonious (opening) or disharmonious (banishing). *Memory Body Essays*. In the book you'll learn how ANY and all stars can be classified as harmonious or disharmonious.
In the beginning was the number #150; and the power of numbers begins ..
The perfect star families of numbers introduce some changes to our perception of universe building and **thesis vub** how everyday reality happens to come about.

Mathematicians can make all kinds of star constructions, in 2D and 3D #150; but only the perfect star families can begin to bridge the **memory essays death** straight line energies, such as photonic energy, with circular orbits and orbital energies. *Richtlijnen*. Because the vast majority of the real energy in the universe is in the form of spinning or orbital energy #150; that is, energy having angular momentum, the perfect star families of numbers take the front seat. Scientists can draw all kinds of curves but these are usually fancies. Mathematicians in *on laughter* particular insist their work has no bounds, yet in their hearts they know their discoveries should have some practical application.
Starting with 24 hours per day and having 80 minutes in an hour, every minute of every day (24x80= 1920 ) would divide a circle exactly. Such is not the **richtlijnen thesis** case today. After that, a binary number 1024 would stand for seconds and continue to divide the day's circle exactly. One of the **essay club** new seconds would then be the exact 1,966,080th part of a day. The new second would be somewhat faster than one twentieth of the present second (0.05). While adequate for almost all sports without further division, additional circle-exact divisions are always available #150; something that is not possible to do today. (Once you lose the exact circle division it cannot be recovered.) The sweep of the seconds hand would be 1/3 faster than the present sweep to make one full revolution in *vub* 1/80th of an hour.

At all numerical markings in the illustration on **essay club**, right #150; the hours, minutes, and seconds #150; would not be fractions. For example, the sweep of the seconds hand spanning one half of the quadrant adds up to thesis vub 128 seconds .
One half quadrant, then, is 128 seconds or 10 minutes or 3 hours. The new minute count of 80 per **essays** hour divides a circle exactly and using 80 points around the circle can make the **vub** perfect 4, 5, 8, 10, 16, 20, 40, and 80 pointed stars. From the 24 hour clock face one would make the perfect 3, 4, 6, 8, 12, and 24 pointed stars.
A pentagram star is **essays theatre death**, harmonious (opening in Wicca speak) if drawn counter-clockwise and disharmonious (banishing) if drawn clockwise. Once you understand the harmony/disharmony, you will be able to extend it to other stars besides pentagram. Some counter-clockwise 8 and 10 pointed stars are harmonious but these stars are disharmonious if drawn clockwise. This does not mean the clock's hands rotation should reverse. See the Venus page.

Now, could you come up with another sequence that always makes an exact circle division, both locally (by itself) and **richtlijnen** overall (with respect to the starting circle)? Yes. *Nora Ephron A Few Words About Breasts*. Start with 20 hours per day and divide each hour by 192 minutes. *Richtlijnen Thesis*. Both 20 and 192 divide a circle exactly but, in addition, 20 times 192 is **body essays**, 3840, which also divides a circle exactly. Is there more to this than making new and different watches? You bet.
Tiling of pentagons and stars.

Tiling does not involve direct construction but only translation and/or rotation in two dimensions. Translations are linear (straight) motions. The line provides symmetry about *richtlijnen thesis vub*, a (such) line [feminine] while rotations are always symmetrical about a point [masculine]. *Law Assignments Essays*. This does not seem like a big deal but the property that allows (in this case pentagon's) translation or rotation to get to richtlijnen thesis vub an identical solution is exceptionally important in universe building (and in *nora ephron words breasts* the group theory, too) .
Tiling of five pentagons to make a cool five pointed star was (first?) published by *thesis vub*, Kepler in Harmonic es Mundi (1619)
When the ancients instructed us to use the straightedge and compass, they were not really talking about constraints because they were talking about geometry.

Rotation about *amusement park*, a point is **richtlijnen vub**, about the use of the compass. Straight movement (translation) is about a symmetry about a line and perhaps you could see now that the line of symmetry is a virtual line #150; that is, the **essay** line of symmetry is an empty slit. *Richtlijnen Vub*. (Would you go as far as to have Justice brandishing her sword with a slit down the middle of the **law assignments** blade?) The virtual line has powerful geometric properties but you do not want to ask a woman about that. Not that you couldn't, it's just that the explanation is nonverbal.
The pentagon template for the illustration on **richtlijnen**, the left was obtained with MS PowerPoint by *memory essays theatre*, selecting AutoShapes .. Basic Shapes. Pick the **richtlijnen thesis** pentagon object. On the newer versions it is Insert .. Shapes .. Basic Shapes.
If you tile five pentagons you get the five-point star in the center. Now, if you take five five-point stars and arrange them around with their points touching, do you get a pentagon in the center? You always want to test for reversibility , even at the expense of appearing dyslexic. Relations are reversible only under certain conditions and **memory theatre death** you want to know what they are.

If you assume relations are always reversible as they are in *richtlijnen thesis vub* algebra, you will 1 ) understand but a limited subset of reality [if you are lucky] and/or 2 ) misinterpret relations that are not reversible.
For example, if there is **nora essay a few words**, a quantum mechanical explanation of gas pressure, there could be a way of making the phenomena reversible. Now, how would you reverse the rotation of a light mill? (Give it a thought and get the answer .)
We readily apply force to get things moving. *Vub*. So, how would you reverse 'something' and have the force arise?
A circle of stars, a pattern of stars:
Testing for reversibility is crucial in the understanding of relationships. Dyslexia is a condition that is **law assignments essays**, constantly reversing relationships in all modalities: verbal, tonal, geometric, written -- to see if the reversal possibly acquires another meaning, or if the reversal carries no meaning.

The Quantum Pythagoreans book treats the **richtlijnen** difficult topic of relationships by novel exploration of dependent-independent properties of a relationship. You will then understand and normalize the difference between, for **essay on laughter club**, example, 'planning your work' and 'working your plan.'
The tiling construction #151; that is, movement about a point and/or translation along a line, of some objects may result in the appearance of another object. This is at times referred to as negative space. While it is **richtlijnen vub**, true that the original object is real and in some respects positive, the **essays** 'negative space' label is **thesis**, but an law assignments essays, introductory way of looking at it (and a left-brain way at that). *Vub*. A good way is to gpa on resume see this as the act of *richtlijnen vub* creation of the virtual object .
When working the Great Pyramid, you may want to think of the chambers and passageways as virtual objects or empty-space objects. It really helps.

Self test:-) Straighten up two adjacent fingers. Do you see a difference if you think of these fingers as two closely spaced pencils #150; or as an empty slit or space that is between the pencils? Photons and **paper on identity** electrons do, for they make very different patterns for a single bar, two bars, a single slit, or a dual slit.
For brainwork: 1 ) How is it possible, and 2 ) What is the utility of the **thesis vub** result that one pattern ends up in the left side of the **paper** brain while the other in the right side?
Ancient Greek-speaking scholars debated geometry and arithmetic, and understood the complexities even without a PC.
A circle is an angle (of 360 degrees) that is divisible by three exactly using geometric means. This result is significantly more interesting than the mainstream mathematicians' proof that an angle is not, in general, divisible by three.

If you think of a circle with the orbit (cosmic) and/or orbital (atomic) applications in mind, you will see there is **thesis**, lots of fun in figuring out what works[, rather than beefing up your resume with things that don't]. So, the ancient riddle about dividing the **paper** angle into thirds has more than one answer and no answer is the wrong answer. *Thesis Vub*. It is, however, a parting, or the Tau riddle that to some makes all the difference. But again, no angle can be divided by three exactly arithmetically. No angle can be arithmetically divided exactly by any rational number even if such angle was first obtained geometrically and exactly.
A circle cannot be divided by 7 or 9 equally and exactly.

This fact may lead to body essays some new discoveries but if your skills are mostly in arithmetic you'll likely think of it as a curiosity. That is the basis of reductionism, for a reductionist first makes a claim that arithmetic is just as good as geometry (brain grouping), and then happily ignores the advantages of geometry. *Richtlijnen Thesis Vub*. Similarly, equating irrational and rational numbers is erroneous but the mainstream math guys think them equal and **memory body theatre** miss a lot (see incommensurables).
Yet, the best example of the **thesis** power of *memory essays* geometry is in the construction of the so-called geometric mean. Here, the semicircle and the Pythagorean Theorem produce a square root of any rational or irrational number. *Thesis Vub*. Moreover, the **paper** geometric mean can multiply two irrational numbers together and **richtlijnen** produce an exact result, the infinite mantissa and all. *Nora Essay A Few*. No computer can do that.

The bottom line: Geometry always leads, arithmetic always follows.
For example, I came up with a nice infinite series that relates the power (exponent) of the golden ratio to two terms of the numbers from the Fibonacci series F n . What this relation shows is that any power n of the golden ratio a/b can be expressed as a multiple of a single golden ratio a/b .
Initially I called this the IG series for I nstant G old series. I liked the label 'instant' because Kepler got to the golden ratio a/b using the infinite progression of the Fibonacci series F -- but here and **richtlijnen thesis vub** now the Fibonacci is not taken to amusement the infinite limit to get a/b . I also discovered that this equation, in a form a bit different from mine, already exists. After a while and once I figured out what is happening geometrically, I could not help but calling it the **thesis vub** I vsin G old series [yes, thank you], simply because the geometric understanding opens up a whole new world of applications . The arithmetic equation by itself is okay but the applications just do not reveal themselves if you look at it algebraically. *Essays*. Try it yourself ..

In another example, you know that 360 degrees in a circle is arbitrary. Very soon (just below) you'll see why a circle cannot have another number of degrees that would match the power of *richtlijnen thesis* geometry. *Essay Club*. A circle becomes (is) a unitary entity of *richtlijnen thesis vub* its own and arithmetic can deal with a circle only via an infinite series. Having said that, a circle would not be possible to turn into a square #151; but, by using the virtual numbers and understanding the infinite superposition .. .. A circle can be constructed or divided in finite time only geometrically. Moreover, a circle's manipulations must be exact if you want to understand how an atom is or could be made.
It is now time to visit the angles of a circle. Can we map the angles in such a way as to obtain correspondence between geometry and arithmetic?
Arithmetic makes it strange.
In a calculator, the angle of 360 degrees is **adding**, divisible by 9 without a remainder, but this is but an arithmetic computation. In geometry, the circumference of a circle issues from *thesis vub*, Pi, which is a transcendental number and so you cannot be arbitrary about the length of the circle or the exactness of an angle inside a circle. *Adding Gpa On Resume*. Yes, the angle of 40 degrees is **vub**, not constructible exactly because a circle is not divisible by 9 exactly.

But it does happen that a circle is divisible by 40 exactly and then an angle of 9 degrees can be had exactly. Division of a circle into an arbitrary integer quantity of *essay club* equal and **richtlijnen thesis vub** exact segments (or angles) is not possible.
What then is the advantage in *ephron essay a few words* dividing the circle exactly by this or that number? The atom holds together by having electrons wrapping around the **richtlijnen thesis vub** nucleus. Because the **gpa on** electron's momentum is also a wave ( de Broglie ), the electron's wave must evenly, that is exactly, close upon itself to form a standing and a round wave that is symmetrical about a point.

To the Pythagoreans the numbers are everything and this is because numbers actually create things.
The mainstream scientists' argument that computer's representation of an richtlijnen, irrational number is close enough is, unfortunately, not relevant to atomic construction. Scientists just do not know how to law assignments interpret 'precise' and 'exact' in an applications setting. The scientist can divide the circle by nine to a very large number of decimal places, but there will never be a wavelength that would fit nine times around the **thesis vub** circle of the orbital. *Memory Body Essays*. Incidentally, 'fit' is the original (superior?) word for a 'node' that was used by Newton in his description of standing waves. In today's terminology, we would say that a nine-wavelength, or 18-node, standing circular wave cannot and will not happen (will not fit). Numbers 7, 9, 11, 13, 19, 21, 22, 23, 25 and others cannot divide a circle exactly. Most of these numbers are incomposite (prime) numbers. Number 9, though, is a composite number as well as a square number, but it cannot be used to vub divide a circle exactly. [Does this mean the Chinese Emperors could not sing?

Having said that, they might have been good golf players.] Number 5 is incomposite but can be used to divide a circle exactly. *Gpa On*. What is needed, then, is **richtlijnen**, a class of numbers that compose in a circle , instead of just being composite numbers (composed of products of other numbers). These numbers, called circumpositional numbers [by yours truly], are prominent in atomic construction. Above, we introduced these numbers as the perfect all-star family of numbers.
If you don't mind additional complexity, or perhaps simplicity, a circle can be divided exactly only through geometric means.

Another way of saying 'geometric means' is **ephron words about**, 'spatial distance means.' Yes, the **richtlijnen thesis** circumference of a circle is a transcendental number and a division of any transcendental number by any real number remains transcendental (a real number is finite). The computer can use only *adding resume* real numbers and the length of the circumference is then rounded off if it is to be stored in a computer. What this also means is that a computer cannot give you a perfect star. What this really means is that you must have movement to create a perfect star. In other words, you cannot make a perfect star via placement or measurement (statically, topologically) with a ruler or a computer or a computer-calibrated protractor. As a Pythagorean you might realize that you cannot construct a perfect star without a compass #150; that is, you need rotation to complete exact constructions.

A compass is the only tool that allows you to enter 2D from 1D. In other words, a compass allows you to turn. A larger implication is **vub**, that there must be movement even at the atomic core level #151; and under radial symmetry the movement is also about frequency. (You might guess here is **amusement park**, one of the gateways to gravitation and **thesis** yes, the philosopher's stone opens up to the alchemist.) The necessity of movement permeates everything. Even the ability to square a circle appears like basic stuff when developing (Tai) Chi in your body (think 3D).
Arithmetic makes it practical.
Pythagoreans had a category of numbers they called 'abundant.' Such numbers are evenly divisible (without a remainder) by many other numbers. Number 60 (minutes in an hour) is **research**, a good example as it is divisible by 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 -- which, not incidentally, are the number of points of stars one can make with minute watch face markings. Another convenient (abundant) number is **richtlijnen**, 24 (hours in a day), but we presently divide the day only by 2 (am and pm) and by 3 (work part), and possibly by 12 (entertainment).

Facilitating easy workings in the geometry of *memory body essays theatre death* a circle, however, calls for a more abundant number. If you were to come up with a good working number for **vub**, the total number of *adding resume* degrees in a circle, you may find 360 to be a very accommodating number. 360 degrees of a circle divide evenly into quarters (possibly the most important requirement right next to 365 days in a year). It divides evenly by 5, 10, and 20, too. *Richtlijnen Thesis*. You've already noted that the **essay on laughter** division by 5 (and consequently by 10) is very practical because a circle division by five brings in the golden proportion. The practicality of this number won the **richtlijnen** day even though 360 is **gpa on**, also evenly divisible by 9 and a circle cannot be divided by 9 exactly. If you were a stickler for details such as this, you most definitely would insist on 2040 degrees in a circle. 2040 is evenly divisible by 2, 3, 4, 5, 6, 8, 10, 15, and 17 -- all numbers that divide a circle exactly through geometric means. The good old 360 is not evenly divisible by 17 and that means that exact geometrically-obtained angles do not necessarily have a corresponding whole number of *thesis* degrees if we stick to the present 360 quantity notation.

Both 360 and 2040 are not evenly divisible by 7, 11, and 13 -- as it should be. But 2040 is also not evenly divisible by 9, and **paper on identity** we have even better correspondence between geometry and arithmetic. *Richtlijnen Vub*. The year 2040 could be the **essay a few words about breasts** most harmonious year coming up. [But don't tell IRS. *Richtlijnen Thesis*. They'll put this number on a form and spoil it.]
Now that all people are smart enough to handle as huge number as 2040, is it time to make our circle geometry as sophisticated as it can be? Are you ready for the sum of internal angles in *law assignments essays* a triangle to equal 1020 degrees instead of 180? And the internal angle of an richtlijnen thesis, equilateral triangle would be 340 degrees instead of 60?

Even if you could legislate the **gpa on** change #150; and during the French Revolution they legislated 100 degrees in a circle and **richtlijnen thesis vub** 100 minutes in an hour -- the **essay club** bottom line is **thesis vub**, that there is **ephron a few words breasts**, no perfect number for a quantity of degrees in a circle that would be a whole number or even a rational number. That is, there is no number that would be evenly divisible by those numbers that divide a circle exactly geometrically. In the example of the **thesis** 2040, this number is not evenly divisible by 16. [Some Masonic authors give Freemasons credit for leading the **law assignments** French Revolution. If so, they would certainly be quite ignorant on what to do in *richtlijnen thesis vub* the aftermath #150; all their Gs notwithstanding.]
Whole numbers and rational numbers are called real numbers #150; a good name. An incommensurable (transcendental or irrational) number can never become a real number unless it is transformed . The transformation is irreversible because we cannot save an irrational number such as SQRT(2) in a computer and retrieve it as (convert it back into) the original irrational number without first taking a nip off the number #150; think Ouroboros and visit Circle and Pi . Reversing the transformation calls for addition of the virtual energy [think Isis and **nora ephron essay a few about breasts** possibly Thoth if you are familiar with his eye restoration story].
If you want to richtlijnen vub get deeper into transformations of rational (real) and irrational numbers #150; think ancient Egyptian fractions [here, you will need to appreciate three things: 1 ) Ancient Egyptian fractions are quite sophisticated; 2 ) Present day scientists are clueless as to the ancient Egyptian fraction applications or origin; and 3 ) Our present civilization is not necessarily advancing.]
When dividing a circle with the straightedge and compass, the goal is to make the number to become , for the number's geometric construction creates something specific to that number. There is, then, more to numbers than philosophy, and you may want to visit the original number apps guys, Pythagoras and his fellow Pythagoreans . There is a treatment there of *essays* real, virtual, and irrational numbers. Irrationals and transcendentals are in the family of incommensurables but transcendentals are not constructible through the Pythagorean Theorem (from 2D of the **thesis** curve to 1D of the hypotenuse), while additional differences between irrationals is based on applications. [There are good and bad numbers and some of them have an infinite mantissa.]

What does a star in a circle represent? What is the meaning and symbolism of a star inside a single circle? The point count of the star is about the wavelength multiples that curve and create the **nora ephron a few about** atom. *Richtlijnen Thesis Vub*. Don't bother with scientists' point electron orbiting core pictures, for **essays**, atomic electrons are really standing waves having point symmetries (symmetry about the core). As always, you will need to learn which stars are geometrically constructible and can be actualized, and which are just the **richtlijnen vub** arithmetic's (or computer's or religion's) fancy.
Is the atomic core composed of standing waves? You bet. Scientists have way too much invested in *essay on laughter club* the solid and static core hypothesis and so it is safe to talk about the pulsing and standing waves of the core. Scientists are way off and, for example, they made up strong nuclear force because they do not understand the wave nature of the core. In a way this is okay, for you can make many advancements while the scientist remains clueless.

For example, the core's shape is not necessarily spherical.
With all their equations, scientists think highly of whatever it is they describe with them. Saying that the scientist will remain clueless is no idle talk, however. On our Circle Pi page we also highlight the inadequacy of algebra, for **richtlijnen thesis vub**, algebra's constructs cannot deal with the operation of equivalence. Algebra completely misses irreversibility, too.
As a Pythagorean you want to memory body death figure out **richtlijnen thesis vub**, what entity will prevail in the interaction with a standing-wave electron and with a standing-wave proton. Why, could you then do a precision surgery on the atom?
Seven pointed star.
A circle cannot be divided by *law assignments*, seven exactly.

Yes, we can say that seven people cannot share a round pizza equally, and leave it at that, except that the **richtlijnen vub** number seven is the first number with such property. When things are happening inside a circle #151; that is, when things are spinning and evolving, the **nora essay a few** wave folding encounters the number seven and consequent inability to fit around the circle (and make a perfect star). When you examine the **vub** Mesoamerican Hunab Ku symbol, there are two seven-sided areas (heptagons) and now the challenge is to explain that. The seven sides are not drawn equal in length and that gives the symbol some credibility. The heptagons pivot into **amusement park**, 3D and now it gets really intriguing. If we don't take the **richtlijnen** Hunab Ku (some say Hanub Ku) as a product of coca leaf-chewing fancy, there are many interesting things happening around the number seven.
I'd be careful in using the seven pointed star. Adopting a regular heptagon or a regular seven pointed star shows you don't get it.

So I'd draw the star free hand or use an on identity, irregular heptagon. Mayans have a gap in their seven-segment Ouroboros too.
The Goddess Seshat's symbol from ancient Egypt is a contextualized seven-leafed plant (she is **richtlijnen**, a scribe, which means she is a magician). The leaves spread out in a star configuration, but the resulting seven pointed star is not regular. *Club*. [If you think the symbol is a cannabis plant then that's fine by me. However, geometry prevails (has priority) while cannabis also has 5 and 9 leaf varieties.]
The Statue of Liberty has a hair dress with seven rays. The symbolism of her 7-point star is rich with 'seven seas' and 'seven liberal arts' interpretations, but I prefer to look at it geometrically and enjoy the fact the rays are not regular.
The wonderful part of the circular geometry is that it needs to be treated separately and carefully. Euclid may have proved that no two Natural numbers (integers) when put in *thesis* a ratio will result in an incommensurable (irrational) number. But some incommensurable numbers when put in the ratio (or are proportioned) could result in a rational number. You may want to reflect on what it means.

As far as Euclid goes, not much. After all, Euclid talks about what does not happen. But what does it mean when transcendental -- that is curving -- and straight line (ir)rational geometries meet at certain points? Think transformations and visit the Proofs page that talks about the squaring of a circle.
Understanding the angles in a circle certainly takes you to another and very substantial pursuit of universe building. Looking back, is there some work that was done just in *essay on laughter* this area? But of course, you'll have to step over the reductionists, yawn at the popularizers, and laugh at vub people who allow to be called experts. *Ephron Essay Words About*. [I'd bet 10:1 they will talk about *richtlijnen thesis*, running out of energy.] The ancient Egyptian fractions have the numerator expressed as an oval having the value of 1 . It is a symbol for a unitary entity that has symmetry about a point such as a circle or an ephron about, ellipse. *Thesis*. And if you have two circles that you want to divide into sub-unity fractions, are we really talking about two atomic orbitals and the possible (energy) fractional values they can acquire during an electron jump? So now you have yet another quest to make. *Paper*. A road where you will also discard all the modern mathematicians musing at the awkwardness of the ancient Egyptian fractions.

The Rhind papyrus has the 2/n expansion and **richtlijnen thesis vub** now you know what the 2 is **paper**, about.
Riemann sees a sphere with longitudinals that, with identical curvature, converge and meet at thesis vub the poles at resume finite distance where they close upon vub, themselves (think atomic orbitals in a closed 3D topology). *Gpa On*. Although Riemann, a math guy, did not have an atom in his mind, his geometry is 'parallel yet finite.' He discovered an richtlijnen, unusual way of obtaining all incomposite (prime) numbers. *Law Assignments Essays*. We have three book reviews on this remarkable individual.
Then there are the scales of the **richtlijnen** fish [yeah, the dumb fish]. The sweeps of the **nora a few** scales subtend a particular angle.

Do you think a fish could fly or extract energy from the **richtlijnen vub** swirling water around it by using the geometry of its scales? In reverse, could you work the straight-moving energy to close upon itself and make an atomic orbital? Think pyramid geometry and Schauberger .
Illuminati, Masons and New Order Guys. Pythagoreans, too.
Symbolism is about associating something with something similar. Pythagorean logic, for example, says that two points make an axis and then the number two is behind the mirror symmetry, aka the axial, even, or feminine symmetry.

As a Pythagorean you have no problem with that, and wouldn't use the term axis of *paper* evil because both the constructive and **richtlijnen thesis vub** destructive energies exist about an axis (about 1D). You'd then apply one point of 0D as the source for rotation and consequent (odd, masculine) symmetry. But you are also smart enough to figure out **about breasts**, that after 3 points (of volume) you enter a different, virtual domain that is **richtlijnen**, based on the number 4. Associations can go on and on and are thus unbounded, and in *essays* a fine distinction the associations become infinite relationships. So now you can relate and associate from here to eternity and each time you may get to thesis vub a different conclusion. You can now perhaps see the possibility of making something bad or evil out of *paper* something that is pedestrian or even boring.
So you want to richtlijnen vub ask if the result you reached is beneficial or not. If you think accusing someone of evil thoughts is beneficial to your religion then you are a part of a religion that is sustained by attempted oppression of others. *Essay Club*. In short, your religion is not based on truth. In fact, all possible thoughts and all knowledge exist in *richtlijnen* infinite superposition with each other and **essay club** is to a greater or lesser degree available to you. You are never fully locked out from knowledge you seek, but its usefulness may not be obvious.
If you keep an open mind you will soon discover that working with infinities is no easy matter.

Shutting down your mind (narrow one's mind) is **vub**, a defensive reaction to an onslaught of information. You may even figure out that all religions attempt to understand infinities and could well be defined just by that. So relax. Infinities can be worked but they need different methods. Things that don't add up simply won't happen.
[So what is my Pythagorean take on **research on identity**, the 7-point irregular star? It is **richtlijnen**, about the creation or release (liberation) of energy.

As with anything it could have a down side, but with superior assistance (God?) it can be managed and be useful. Oh, the thing about God is that you have to ask. *Resume*. It's not because God is busy, but because you get a specific answer to vub a specific question. *Essays*. Most importantly, you will never get an richtlijnen thesis, order or a command: only knowledge. *A Few Words About*. The action (or non-action) is yours and **vub** is based on your free will and **amusement park essays** your consequent responsibility for your actions.]
Johann Balmer was the guy who opened wide the **richtlijnen vub** barn doors of quantum mechanics. Fifteen years before Planck , he came up with the relation that produces a sequence of numbers matching the wavelengths of light coming from hydrogen. These are not just any numbers #150; they are wavelengths corresponding to particular electron jumps and no other.

Balmer did for quantum mechanics what Kepler did for gravitation: He came up with the math equation that matched known experimental data and made successful predictions of *research paper* other new, yet undiscovered, wavelengths. But there is a bit more to it. Balmer used integers and square numbers in his relation that were those of the **thesis vub** Pythagorean Theorem. *Memory Body*. Well, good ol' Pythagoras was not only right all along but the breadth of his #150; some say HIS #150; teaching was also the **richtlijnen** foundation of *essay a few about breasts* quantum mechanics. Natural numbers and his theorem are also the source of the quantum behavior of atoms.
This topic is expanded and has a page of its own. To reconcile the straight (1D) and the curving (2D or 3D), you will be dealing with the squaring of a circle. Algebra works fine when things are straight or polynomial or exponential. Generally, however, when geometry picks up another dimension and lines start to be circular, the **thesis** equations are not enough as the **research paper** transcendentals come up.

The relationship of the squaring of a circle to this page's perfect division of a circle is in the possibility of *richtlijnen thesis* linearizing the curved segments (arcs) of a circle and then making a tractable exchange between curving and **ephron essay a few words about breasts** straight topologies. So there is a continuation to 'how to draw a star' and it deals with energy. Can we say that geometry is about energy? Can we say that the exactness of particular geometric solutions goes along with the exact conservation of energy? Of course, Pythagorean methods are used to find new ways while mainstream science continues to be arm chair science by playing up one trivial answer as the only answer. At times politicians pick up the **thesis vub** 'square a circle' analogy and then you should know they are trying to ephron essay a few words about breasts find excuses and explain failures to their supposedly dumb constituents. So, even though the squaring of a circle is not possible using real methods , the squaring of a circle is possible.
The complexity of our environment is oftentimes worked through alchemy.

There is a method behind the **richtlijnen vub** seemingly strange associations and we offer the **nora breasts** interpretation of The Emerald Tablet on our Alchemy page.
Summary, Cosmic (Macro)
Pythagorean discovery of irrationals spawned the urgent pursuit of geometry lasting over 2400 years. Kepler brought arithmetic to richtlijnen thesis the forefront by *essays*, establishing the mathematical and arithmetic relations of heavenly orbits. In effect and in fact, Kepler introduced the parameter of time in *vub* the mathematical context, which made it possible to gpa on make planetary position forecasts #151; forecasting being Kepler's life long passion. Because any two gravitationally interacting bodies always have a solution, the **vub** parameter of time derived from such periodic solutions is also repeatable (periodic) and time can be used to make forecasts. Even though time is always a derived (dependent) variable, the mathematical solution establishes reversibility and allows the time parameter derived from this system to be used. (The equal sign indicates reversibility but reversibility is by *resume*, no means a given.) Another way of seeing the mathematical solution and **thesis** consequent time reversibility is that the spatial distance (space) and time form an overlay. In a chaotic system, or in a non-periodic system such as the free economy system, the parameter of time cannot be used to make predictions.

Geometrically, you can take any square and construct another square that has exactly twice the area of the original square. A square can be increasing in *theatre* infinitely small increments, including irrationals, while the doubled square follows that exactly (think conservation of energy of a moving object). This is something your computer cannot do. If you think this is no big deal and it is **richtlijnen vub**, something for the ancients to contemplate #150; that's fine. The gateway question that makes all the difference is: Can you construct infinity? Certainly the **on laughter** most enticing question is: Can you stop moving bodies at a distance?
Light is understood as moving or standing linear -- that is, straight, waves following Newton's analysis of fringes (first observed as fringe rings). As light becomes closely associated with matter, Balmer kicks off the QM atomic pursuit with a Pythagorean relation. A wavefunction is **richtlijnen vub**, understood as a probability distribution of an atomic particle #151; a great step forward by Heisenberg and von Neumann.

A moving particle has momentum but momentum can also be worked as a wave #151; a second great step, this time by de Broglie. A moving electron now gets to ephron essay a few words become a wave as well, but this wave must curve #150; that is, become circular , and close upon itself in a symmetry about a point (about a core). The circular (or rounded) electron orbital and the straight path of light need to be energy-reconciled through the squaring of a circle #151; the first difficult hurdle.
Ether is **thesis**, taken out of *essays* science's purview, which is the Great Reduction making the scientist that much poorer in *richtlijnen thesis* the end. Scientists cannot make headway and talk about impossibilities. They reduce everything until there is no intelligence in their design and take an early exit. (In their last hurrah the angry mob bashes and trashes cold fusion.) Scientists thus successfully reduced themselves into a group of believers in 'light-is-real-and-puts-pressure-on-mirror.' While much of today's physics rests on it, the scientist has no guts and **memory body essays** no brains to perform the **richtlijnen vub** actual experiment measuring the presumed pressure light puts on a mirror. Scientists are not able to face up to the truth that a light beam does not and **essay club** cannot put pressure on a mirror and so they are stuck perpetuating, defending, and proselytizing their dogma.
Meanwhile, geometry is receiving new impetus by reviving its superiority over arithmetic and algebra. The golden proportion, the **richtlijnen thesis** infinite and instant wavefunction superposition, the **adding gpa on** understanding of irrational and transcendental numbers, linearizing particular segments of a circle, and the possibility of creating electron waves with harmonics-series energy components just might get the atomic understanding going again #150; perhaps in another country, perhaps by another group of *thesis* professionals.
The cosmic (or planetary) pentagram and the five fold atomic orbital make the five pointed star a joining symbol for both the macro and the micro.

While the atom's orbitals are symmetrical about a point (have radial symmetry), the valence orbitals in a molecule need to close around two points of symmetry (the cores of the atoms are some distance apart). Yes, the Hyper s tar has an answer to that on our golden proportions page.
Self-test:-) If you are not happy about the pentagon base and/or the pyramid being split up or broken up or separated, you are not getting the picture. *Park Essays*. You may want to think about the red part as being the tangible component while the blue part is the intangible (knowledge, virtual) component. If that does not help, stay in 2D [earthbound?] where the pentagon is continuous.
If you think Two rather than Four is feminine , you are very close. You will need to appreciate that the virtual variables are double-ended and **vub** have opposites. Then you'll need to center these variables to relate them in *essays* infinite superposition. ( Quantum Pythagoreans book helps in this area too.)
The engagement of *richtlijnen vub* Three and Four is just that: It can be supportive in some contexts and in others it could be conflicting, in which case rebalancing work is needed.

So, the **essay** recommendation for The Pentagon is to modify one of the pentagons (or build a new inner one) to reflect the separate golden trapezoid and **thesis vub** the golden triangle. The new construction slants upward toward a point. *Essays*. It does not need to top off in *richtlijnen* a point as long as the edges are converging toward a point. (If it does top off, think about the straightness of the edges -- it ain't straightforward.)
This pentagonal pyramid is on **nora ephron essay a few words about**, Mars. The picture credit most likely goes to NASA although I don't know the particulars of image enhancements processing -- none or too much. *Richtlijnen Vub*. Note the pentagonal aspect is **resume**, not regular (a point-to-point straight line over a ridge and through the **richtlijnen thesis vub** center can be made).
There is **body essays**, one symbol that uses a circle framed by two vertical lines. These lines are at richtlijnen times shown as two (usually) identical posts or columns.

At other times it is **essays**, shown as a person holding two vertical sticks, candles, or wands. This symbolism, however, is not about the 3 vs. 4. *Vub*. Rather, the two lines or sticks or columns are about the virtual line of the even symmetry that is relevant to the virtual domain and the energy therein. The upcoming book (late 2013) deals with the construction in the micro domain via the **on laughter** stars, the rings and the symmetries. Yes, knowledge is organized energy.
Three and Four must remain separate even though they are also joined. You can then see it as a five sided pyramid made from *richtlijnen vub*, two pyramids that each have unique properties. The overall 3D structure has almost all numbers in it but the point is that the numbers must play together to their best advantage (rather than just being represented).

Do you see the number zero? Or is it the infinity? Could it be both? Is the number zero combined with infinity the source of the Pythagorean fire? The root of the pyra-mid? The Central fire? The hearth of Zeus? Archimedes' fulcrum of the heaven and the earth? Just a plain (free) electron?

The convergence of the north and the south poles on decreasing Riemann sphere? A point of the **research paper** zero dimensional (0D) geometric construct? 'The One' of alchemy? Something even smaller than the infinitesimal of *richtlijnen thesis vub* Newton and Leibniz? The dot in the semicircle on the AUM symbol? A computational construct for all of the above from all of the **nora essay words** above? The top dot of Tetractys? My favorite : The eye Thoth sends to look for Tefnut when she runs away to richtlijnen Nubia (yes, the eye finds her).
If you think this pyramid is about marriage, you are on the right track.

The Three [male] and Four [female] are joined through the point of the **adding** infinite. This joining is applicable to the actual marriage where the **thesis vub** joining is **essay**, through God #150; all there is. The alchemical marriage would have the female part becoming more abstract although the **thesis** four-sided pyramid geometry continues to be needed for **essay**, dealing with the infinite. *Thesis*. You are, perhaps surprisingly, also looking at on laughter club the joining of matter at the atomic or micro level.
The virtual component (in sky blue here; would be white for **richtlijnen**, the ancient Egyptians) has the golden trapezoid for its base, for the longer to the shorter sides are in *adding gpa on* the golden proportion. The real component has one of the golden triangles for its base.
If you like alchemy, the triangular pyramid is the **thesis vub** king (or sun, gold) while the four-sided pyramid is the queen (moon, silver).

Yes, this is the 3 vs. 4.
In the ancient Egyptian context, the crown of Egypt has two separate components: The white (upper, virtual) and **park** the red (lower, real). The gap between the two is the ancient Egyptian blue crown and is invoked at richtlijnen war. *Law Assignments*. (The gap is white in our pentagonal pyramid.)
Book by Mike Ivsin.
Pythagoreans use the knowledge of numbers to thesis arrive at on laughter harmonious and stable systems. Numbers' properties under different symmetries yield specific solutions. Numbers create the duality while the engagement of the duality's components leads to thesis vub organization.
Quantum Pythagoreans applies the Tetractys construct and that results in all observable cosmic topologies. The book describes the nature's computational mechanism, especially as it applies to waves.

What it takes to transform energies. Your body is a component and **memory body essays death** it is not the only one. The shapes inherent in *richtlijnen thesis* the human body have certain geometric context that is **adding gpa on**, revealed in the book and **richtlijnen** it is about your health, too.
You will like and appreciate the simplicity and the power of *research* numbers. *Thesis Vub*. The Pythagorean management of numbers takes you on the road to reality and invites you to essays drive it as well.
Go or select another topic from the gold post.
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Culture and *thesis vub* Mythology/ The Aztecs: A Case Study term paper 18694.
The Aztecs are an ancient culture that had many customs and rituals that by modern standards are considered barbaric. Memory Essays Theatre Death. Their culture was made up of different social classes, and was primitive yet very advanced. They were located in the mainland of Mexico, and their empire was quite vast over that area. Their culture began around 1100, and ended around 1520.
The exact numbers of the Aztecs is not known due to the age of their culture, but judging by the size of thesis vub, their empire it was quite large. The only figure I could find was that in 1519 there were more than 1,000,000 people living in the civilizations boundaries.

The reason that I was drawn to this culture was some of the practices that they had. The most interesting being the *essays* human sacrifices to the gods, and the large ball game that they played that sometimes went on for days without a stop.
The Aztecs lived primarily in a fertile volcanic valley of richtlijnen, Mexico where they built their capital city named Tenochtitlan. The land in which they lived was a plateau seeing that most of the surrounding was mountainous. The soil in the settled areas was very rich and good for **nora a few**, growing crops, due to the volcanic eruptions that occurred. The valley of vub, Mexico was the heartland of Aztec civilization. It is a large internally drained basin surrounded by volcanic mountains that are as high as 9,000 ft in elevation. Thousands of years of amusement essays, soil erosion had produced deep, rich soils in the valley and a system of shallow, swampy, salt lakes in its center. This gave the *richtlijnen vub* Aztecs a diverse variety of foods that could be available. Resume. The salty lakes made available fish, turtles, insect larvae, blue-green algae, and salt. Richtlijnen. The food that was eaten by *essays* the Aztecs varied by social classes.

The peasants lived mainly on corn and beans, except for **thesis**, a duck or a crow that they may have trapped in their garden. Their only *essay*, domesticated animals were rabbits, dogs, and turkeys which were fattened and eaten on special occasions. Corn was the main food of The Aztecs and many foods were made fresh daily from it. Every morning the woman of the family would grind up fresh corn, and make bread for **richtlijnen vub**, the day. The higher classed people, however, enjoyed eating turtles and crabs imported from the coast. It was odd to *research paper*, the Spaniards to find that one of the delicacies of the *thesis* Aztecs was dog.
Aztec homes also differed by social class, peasants built their huts around the edge of the city.

While handymen lived nearer to the center in mud-brick houses. In each of these homes there was normally a mudbrick tub, and they all consisted of a single room. Nobles that were higher in society lived in palaces built of whitewashed stone, and with over a hundred rooms, and were built around the main plaza. Inside of research, all houses the rooms were almost bare, light came in from wooden torches and *richtlijnen thesis* round the room were stored the family’s possessions and objects of daily use. Even palaces had no doors but instead had cloth hung over openings, this allowed for cool air to circulate throughout the house.
For the Aztecs clothing was way of showing social status, so there were very strict laws about *words about*, who could wear what. An ordinary citizen wore a loincloth and cloak, which had to be made of plain undyed maguey-fiber cloth. And if they were caught wearing sandals in the palace they were put to death.

Nobles wore cotton cloaks with borders of precious stones. Craftsmen were able to dye the cotton green, and other colors; they also wove geometric designs into their cloak to symbolize their status in the culture. The Aztecs loved to wear jewelry, but there were also strict laws about this. Most people pierced their ears to *richtlijnen vub*, hold plugs of shell or polished stones. Nobles were allowed to *memory body*, wear gold and carved precious stones in their lower lips to show their high rank. Thesis Vub. Farmers were among the lowest in the dress, they slept in **amusement park** their loincloth, and in the morning he got his blanket and tied it around his shoulder and *richtlijnen* he was dressed. Women wore a woven blouse with an embroidered skirt that held it in place. Every class also had their own haircuts varying from highest to lowest for the most festive style.
Through my studies of the Aztecs I was shocked to find out how much dress, and appearance had to *essays*, do with social status.
The economy of the *richtlijnen vub* Aztecs was largely one of bartering (trade).

The trading was of many goods; this is how the *nora about* large open air markets operated. In the central market there were 4 hierarchal levels or marketplaces. These marketplaces were an area of richtlijnen vub, bustling activity while they were open. The reason that these were so busy was that they were only open for **on laughter**, and Aztec week (which is 5 days). While the market was open there were many stands set up where merchants paid a small fee to *thesis vub*, operate a stand to *adding*, sell their goods. At the market products were monitored for quality, and *richtlijnen thesis* if a product was found of bad quality they were shut down. At the same time anyone caught shoplifting was taken to the court at *law assignments essays* the market, and found guilty.

The punishment was being beaten to death on the spot. The currency that was used was cacao beans for small purchases, for larger purchases the Aztecs used quachtli (cotton capes of standard sizes). The economic level of the *vub* Aztecs was quite high, and was considered as more sophisticated markets that several other civilizations. Even though there was no official currency they did use objects as money ranging from beans to capes. The only unique feature that I could pick out is *club*, how well the market was monitored by the people looking for quality products. This shows an richtlijnen amount of memory theatre death, sophistication on their behalf, by regulating trade in a way.

The economy was very complex, in the way that all aspects of it were tied together, which made the Aztec empire unified. The economy was highly commercialized and dynamic, but it was not a capitalist economy. There was no paid labor, land was not a commodity to be bought and sold, and there were no chances for investment. Richtlijnen Vub. The markets and the economy were embedded in a rigid system of social classes, and no amount of economic success would enable one to cross class barriers.
The Aztecs at the personal level were taught to act sophisticated, with self-control, while still acting well behaved in **death** public. The Aztec people loved to give speeches and help others with problems.

In the social sense of personal acting they were a very confident people, who were proud of their family. In public they were expected to live and act appropriately to the class that they held in society. The family that the Aztecs lived in is a nuclear family consisting of the mother, father, and children all in one house. The parents of the boy who was getting married arranged marriages within the culture. Men married in the late teens to the early 20’s, while women were married sometimes as young as 10 years old. After the *thesis* bride was selected the wedding date was picked. If the marriage fell on an unlucky day it was thought that it would fail. Weddings took place in **nora words about breasts** 2 parts first with a feast at *vub* the wife’s house, and then a trip to the groom’s house for the actual wedding.

To signify the *amusement park essays* union clothes were tied together to show the unity to *richtlijnen*, the gods. Once young people were married they assumed adult roles, and responsibilities. Essays. Their society practiced monogamy, there were not multiple wife families in the culture. The kinship was mainly handled by *vub* men, and was patriarchal.
The Aztec religion was based largely on a debt that humankind owed to the gods, which could only be paid back through sacrifice and blood letting. The religion focused on agricultural fertility and *ephron essay a few words* worship of the sun, which the Aztecs felt the gods created.

The Aztec religion was a complex blend of traditions, unified by emphases on blood, sacrifice, and *richtlijnen thesis* debt payment. Gods of the Aztec religion had a separate temple where their idol was stored. Several priests ran each temple, along with commoner boys, and people who were studying the priesthood. Priests had 3 main duties; most important was the carrying out of rituals. They also left food for the idols, and kept sacred fires burning. Essay On Laughter Club. The lower priests ran the calmecac, supervised by the tlamacazton and personnel, and also kept the sacred books. Above the tlamacazton were the “fire priests”; these were the priests responsible for human sacrifice rituals. Regular priests assisted at the stone of richtlijnen thesis vub, sacrifice, but only a “fire priest” could wield the lethal flint knife.

The head priest was known as a Quetzalcoatl, who presided at the top of the *amusement* Templo Mayor pyramid, and other buildings.
The Aztec religion called for quite a large amount of human sacrifice ceremonies, which were necessary to *thesis vub*, pay the debt to the gods. There were two different ways of paying back the gods, Autosacrifice, or bleeding oneself. Heart sacrifice was also practiced, which was believed to a higher sacrifice to the gods. Autosacrifice was viewed as an alternative to heart sacrifice to pay back the dead. While heart sacrifice was considered stronger to *essay words breasts*, show the *thesis vub* gods respect. The heart sacrifice took place on *research paper on identity*, a pyramid on the stone altar, the heart of the person is removed, and then the *richtlijnen* head is *law assignments*, cut off and *richtlijnen thesis vub* placed on *essays*, a skull rack on the pyramid. Richtlijnen Thesis Vub. The people sacrificed were not looked upon as mere mortals, but as deities whose deaths were similar to the god’s original deaths.
The Aztecs did not have many myths that were in their culture, but they did have a few on the birth of their culture.

The main myth is of the four suns, in which one main god, created two other gods, who in between the creation of earth, other gods, and people were distributed. Memory Body Essays. The name of the *richtlijnen thesis vub* myth of the four suns comes from the four previous ages of gods which came before the *essays* present set. Thesis Vub. The Aztecs had several other myths in their culture, all of which dealt with creation of objects, and light in the culture.
The Aztecs used many different mediums in the art that they made, the *essay club* most popular being stone sculptures, and paintings. Almost all of the art depicted religious symbols that were very important to the culture. The style of art is referred to as the “Mixteca-Puebla style.” The art that they did reflected their religious beliefs, and everyday life. There were collaborations by many carvers on projects for kings, which were mainly large temples, and pyramids.
The use of richtlijnen thesis vub, music and dance was mainly reserved to religious rituals and ceremonies. Drums were the main instruments mentioned in written works, and in drawings. Some other instruments were trumpets on conch shells, pottery flutes and whistles, and rattles. Dances were both with men and women, in **nora a few about** which they moved in a circular pattern around the *thesis* musician in the center.

Young people in the culture were especially proud of their ability to *on laughter*, dance. Song and *richtlijnen* dance were not widely used outside of ceremonial purposes, unless in celebration. These were parts of the culture, but as most things were it remained mainly a religious practice.
The Aztecs were also one of the *essays* cultures of the *richtlijnen* world that built pyramids. The pyramids were not built as a burial chamber like the Egyptians though; they were built as pedestals for temples. The temples that were atop these structures were very well decorated, with statues of the *essays* deity they were dedicated to in the center of the temple. Although no statues still exist there are written accounts from the Spanish conquerors journeys to the region.
In closing the Aztec culture was a very complex culture, with many rituals and ceremonies. Their culture is *richtlijnen thesis*, a very interesting one to study especially in the realm of human sacrifice, and the brutality that took place. They lived in **memory essays theatre** a polytheistic society where there were many gods, and the number continued to grow.

That was the downfall of the Aztecs and many other great Mexican cultures. For the Aztecs Cortez’ came to explore for Spain, and destroyed and stole a lot of elements from their culture. Cortez’ came at the end of a 52 year cycle of the *richtlijnen thesis* calendar at which the god Quetzalcoatl would return to destroy them. So the Aztecs received the Spanish very well, at that time the Spanish attacked and destroyed the culture. It is funny to *amusement park essays*, think that a culture was destroyed by it’s own religious beliefs. In the end the strong belief in gods led to the end of a great early civilization of the Mexican country. A complex culture as well, which as time progressed became more sophisticated and wealthy. Thesis. The Aztecs were very interesting to study, and they are also an ephron essay words about breasts example how beliefs can be a hindrance to a culture, and maybe lead to it’s demise.
1968.

Everyday life of The Aztecs. G.P. Putnam’s Sons, New York, NY. 2. Crosher, Judith. 1976. The Aztecs- Peoples of the past. Silver Burdett Company, Morristown, N.J. 3. Hooker, Richard.

4. Vub. Stuart, Gene S. 1981. The Mighty Aztecs. National Geographic Society. 5. Townsend, Richard F. 1992. The Aztecs. Thames and Hudson Inc., New York, NY. 6. Smith, Michael E.

The Aztecs- The Peoples of America. Blackwell Publisher Inc. Cambridge, Massachusetts. 7. Vaillant, George C. 8. Microsoft Corporation. 1999. Encyclopedia Article. Word Count: 2195. Our writers are all Uni graduates able to work effectively on any level under time constraints.

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