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{{Odd polygon db|Odd polygon stat table|p9}}
In [[geometry]], a '''nonagon''' {{IPAc-en|ˈ|n|ɒ|n|ə|g|ɒ|n}} (or '''enneagon''' {{IPAc-en|ˈ|ɛ|n|iː|ə|ɡ|ɒ|n}}) is a nine-sided polygon.


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The name "nonagon" is a [[prefix]] hybrid formation, from [[Latin]] (''nonus'', "ninth" + ''gonon''), used equivalently, attested already in the 16th century in French ''nonogone'' and in English from the 17th century. The name "enneagon" comes from [[Greek language|Greek]] ''enneagonon'' (εννεα, "nine" + γωνον (from γωνία = "corner")), and is arguably more correct, though somewhat less common than "nonagon".
 
A regular nonagon has [[internal angle]]s of 140°. The area of a regular nonagon of side length ''a'' is given by
:<math>A = \frac{9}{4}a^2\cot\frac{\pi}{9}\simeq6.18182\,a^2.</math>
 
==Construction==
Although a regular nonagon is not [[constructible polygon|constructible]] with [[compass and straightedge]] there are methods of construction that produce very close approximations.
 
Below is a close approximation of a regular nonagon. The approximate angle error is given in the animation.
 
[[File:Approximated Nonagon Inscribed in a Circle.gif]]
 
==Graphs==
The K<sub>9</sub> [[complete graph]] is often drawn as a ''regular enneagon'' with all 36 edges connected. This graph also represents an [[orthographic projection]] of the 9 vertices and 36 edges of the [[8-simplex]]. Three other [[Rectification (geometry)|rectified]] forms also project inside of a regular enneagon:
 
{| class=wikitable
|- align=center
|[[File:8-simplex t0.svg|150px]]<br>[[8-simplex]] (8D)
|[[File:8-simplex t1.svg|150px]]<br>[[Rectified 8-simplex]] (8D)
|[[File:8-simplex t2.svg|150px]]<br>[[Birectified 8-simplex]] (8D)
|[[File:8-simplex t3.svg|150px]]<br>[[Trirectified 8-simplex]] (8D)
|}
 
==Pop culture references==
[[They Might Be Giants]] have a song entitled "Nonagon" on their children's album ''[[Here Come the 123s]]''. It refers to both an attendee at a party at which "everybody in the party is a many-sided polygon" and a dance they perform at this party.<ref>[http://tmbw.net/wiki/Lyrics:Nonagon TMBW.net]</ref> [[Slipknot (band)|Slipknot]]'s logo is also a version of a nonagon, being a nine-pointed star made of 3 triangles.
 
==Architecture==
Temples of [[Bahai Temple|Baha'i Faith]] are required to be nonagonal.
 
The [[U.S. Steel Tower]] is an irregular nonagon.
 
==See also==
*[[Enneagram (geometry)|Enneagram]] (nonagram)
 
==References==
<references/>
*{{MathWorld|urlname=Nonagon|title=Nonagon}}
 
==External links==
*[http://www.mathopenref.com/nonagon.html Properties of a Nonagon] (with interactive animation)
 
{{Polygons}}
 
[[Category:Polygons]]
[[Category:Geometry]]

Revision as of 22:02, 9 October 2013

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What makes the argument that 'essay writing is an art' hold water, however, is the fact that a considerable number of those who struggle with the writing essay task are not necessarily daft people in general terms, but rather people who simply happen to lack aptitude in the fine art that is essay writing. The followings describe what topics you are ready to obtain when you're looking to buy essay paper. The introduction section of an essay consists of the main idea of the essay. And they can ask the kinds of quirky questions'both short answer and full-on essays'that require an element of self-reflection on the part of the applicant. If you adored this article and you would like to collect more info with regards to buy essay college kindly visit the web site. Selection of catchy and precise title will definitely improve the quality of essay.

Write a quick schedule to help you allocate your time wisely: list the days you have left and the time during the day you will be able to work. Persuasive essay also called as argumentative essays are written for the sole purpose of convincing the readers about a particular point of view. This is not often an easy program to enroll into because it is targeted by very many students world wide. "Knowing the truth" behind your recently rejected work will not help. Most of online essay writing companies are there t make money and thus students should be keen when seeking their analytical essay writing help. In geometry, a nonagon Template:IPAc-en (or enneagon Template:IPAc-en) is a nine-sided polygon.

The name "nonagon" is a prefix hybrid formation, from Latin (nonus, "ninth" + gonon), used equivalently, attested already in the 16th century in French nonogone and in English from the 17th century. The name "enneagon" comes from Greek enneagonon (εννεα, "nine" + γωνον (from γωνία = "corner")), and is arguably more correct, though somewhat less common than "nonagon".

A regular nonagon has internal angles of 140°. The area of a regular nonagon of side length a is given by

Construction

Although a regular nonagon is not constructible with compass and straightedge there are methods of construction that produce very close approximations.

Below is a close approximation of a regular nonagon. The approximate angle error is given in the animation.

Graphs

The K9 complete graph is often drawn as a regular enneagon with all 36 edges connected. This graph also represents an orthographic projection of the 9 vertices and 36 edges of the 8-simplex. Three other rectified forms also project inside of a regular enneagon:


8-simplex (8D)

Rectified 8-simplex (8D)

Birectified 8-simplex (8D)

Trirectified 8-simplex (8D)

Pop culture references

They Might Be Giants have a song entitled "Nonagon" on their children's album Here Come the 123s. It refers to both an attendee at a party at which "everybody in the party is a many-sided polygon" and a dance they perform at this party.[1] Slipknot's logo is also a version of a nonagon, being a nine-pointed star made of 3 triangles.

Architecture

Temples of Baha'i Faith are required to be nonagonal.

The U.S. Steel Tower is an irregular nonagon.

See also

References



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