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# pentagon

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.

Related:

Triangle,Polygon, Hexagon, RegularDecagonInscribedInCircle

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Definition

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## Mathematics Subject Classification

51-00*no label found*

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