pentagonPentagon2002-01-05 22:51:132007-07-26 01:11:43Definition\usepackage{amssymb}
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A \emph{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.