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| {{Odd polygon db|Odd polygon stat table|p9}}
| | Hello! I am Susannah. I am happy that I could join to the entire world. I live in Austria, in the LOWER AUSTRIA region. I dream to go to the various countries, to look for acquainted with intriguing individuals.<br><br>Feel free to surf to my website; http://Topelevenhacktriche.wordpress.com/ ([http://www.manosunidasperu.net/2013/07/rockstar-volunteer.html http://www.manosunidasperu.net/2013/07/rockstar-volunteer.html]) |
| 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".
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| A regular nonagon has [[internal angle]]s of 140°. The area of a regular nonagon of side length ''a'' is given by
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| :<math>A = \frac{9}{4}a^2\cot\frac{\pi}{9}\simeq6.18182\,a^2.</math>
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| ==Construction==
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| Although a regular nonagon is not [[constructible polygon|constructible]] with [[compass and straightedge]] there are methods of construction that produce very close approximations.
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| Below is a close approximation of a regular nonagon. The approximate angle error is given in the animation.
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| [[File:Approximated Nonagon Inscribed in a Circle.gif]]
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| ==Graphs==
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| 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:
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| {| class=wikitable
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| |- align=center
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| |[[File:8-simplex t0.svg|150px]]<br>[[8-simplex]] (8D)
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| |[[File:8-simplex t1.svg|150px]]<br>[[Rectified 8-simplex]] (8D)
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| |[[File:8-simplex t2.svg|150px]]<br>[[Birectified 8-simplex]] (8D)
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| |[[File:8-simplex t3.svg|150px]]<br>[[Trirectified 8-simplex]] (8D)
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| |}
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| ==Pop culture references==
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| [[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.
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| ==Architecture==
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| Temples of [[Bahai Temple|Baha'i Faith]] are required to be nonagonal.
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| The [[U.S. Steel Tower]] is an irregular nonagon.
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| ==See also==
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| *[[Enneagram (geometry)|Enneagram]] (nonagram)
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| ==References==
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| <references/>
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| *{{MathWorld|urlname=Nonagon|title=Nonagon}}
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| ==External links==
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| *[http://www.mathopenref.com/nonagon.html Properties of a Nonagon] (with interactive animation)
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| {{Polygons}}
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| [[Category:Polygons]]
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| [[Category:Geometry]]
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Hello! I am Susannah. I am happy that I could join to the entire world. I live in Austria, in the LOWER AUSTRIA region. I dream to go to the various countries, to look for acquainted with intriguing individuals.
Feel free to surf to my website; http://Topelevenhacktriche.wordpress.com/ (http://www.manosunidasperu.net/2013/07/rockstar-volunteer.html)