Octagon

For other uses, see Octagon (disambiguation).

Image:Octagon.png In geometry, an octagon is a polygon that has eight sides.

Regular octagons

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

<math>A = 2a^2 \cot \frac{\pi}{8} = 2(1+\sqrt{2})a^2 \simeq 4.82843 a^2.</math>

In terms of R, the area is 8R^2/(1+<math>sqrt</math>{2}) <p>In terms of r, the area is 8r^2/(11+9<math>sqrt</math>{2}) Image:Stop sign.png

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. Image:OctagonConstructionAni.gif

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.

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.

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