'' In geometry, an octagon is a polygon that has eight sides.

Regular octagons

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A regular octagon is an octagon with equal sides.

The internal angle at each vertex of a regular octagon is 135°. The area of a regular octagon of side length a is given by

$A\; =\; 2a^2\; \backslash cot\; \backslash frac\{\backslash pi\}\{8\}\; =\; 2(1+\backslash sqrt\{2\})a^2\; \backslash simeq\; 4.82843\; a^2.$

In terms of $R$, the area is $8R^2/(1+\backslash sqrt\{2\})$

In terms of $r$, the area is $8r^2/(11+9\backslash sqrt\{2\})$

Construction

A regular octagon is constructible with compass and straightedge. To do so, follow steps 1 through 18 of the animation, noting that the compass radius is not altered during steps 7 though 10.

Octagons in general use

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The most common use of octagons are for the shape of stop signs.

In architecture, an octagon house is a house built in an octagonal shape. Examples include Thomas Jefferson's Poplar Forest, near Lynchburg, Virginia and the Tayloe House (now simply called the "Octagon House") in Washington, D.C., designed by William Thornton for Colonel John Tayloe. The Octagon is a predominent and reocurring theme in Persian Architecture.

In mixed martial arts, The Octagon is the name of the octagonal ring used in the Ultimate Fighting Championship, and by metonymy a term for the UFC itself as well.

The Octagon is the name of the city centres of Bristol, England, and Dunedin, New Zealand.

The Octagon is the name of the Theatre of that shape on the campus of the University of Western Australia, designed by Peter Parkinson after a concept by Tyrone Guthrie.

Oktogon is a major square in downtown Budapest, the crossing point of Andrássy Avenue and the Grand Boulevard.

See also

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• octagonal number

External links

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• How to find the area of an octagon

Polygons

Achteck | Octógono | Octogone | תמניון | Ottagono | 八角形 | ოქტაგონი | Achthoek | Ośmiokąt | Octógono | Kahdeksankulmio | Oktagon | รูปแปดเหลี่ยม