# 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 Pentagon 2013-03-22 12:10:19 2013-03-22 12:10:19 rspuzio (6075) rspuzio (6075) 8 rspuzio (6075) Definition msc 51-00 Triangle Polygon Hexagon RegularDecagonInscribedInCircle