pentagon

A pentagon is a 5-sided planar polygon.

Regular pentagons are of particular interest for geometers. On a regular pentagon, the inner angles are equal to ${108}^{\circ }$. All ten diagonals have the same length. If $s$ is the length of a side and $d$ is the length of a diagonal, then

$$\frac{d}{s}=\frac{1+\sqrt{5}}{2};$$

that is, the ratio between a diagonal and a side is the Golden Number.

A regular pentagon (along with its diagonals) can also be obtained as the projection of a regular pentahedron in four dimensional space onto a plane determined by two opposite edges. This is analogous to the way a square with its diagonals can be obtained as the projection of a tetrahedrononto a plane determined by two opposite edges.

Title	pentagon
Canonical name	Pentagon
Date of creation	2013-03-22 12:10:19
Last modified on	2013-03-22 12:10:19
Owner	rspuzio (6075)
Last modified by	rspuzio (6075)
Numerical id	8
Author	rspuzio (6075)
Entry type	Definition
Classification	msc 51-00
Related topic	Triangle
Related topic	Polygon
Related topic	Hexagon
Related topic	RegularDecagonInscribedInCircle