PlanetMath: pentagon

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pentagon

(Definition)

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 is the length of a side and is the length of a diagonal, then

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

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.

"pentagon" is owned by rspuzio. [ full author list (2) | owner history (2) ]

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Attachments:: pentagram (Definition) by pahio
compass and straightedge construction of regular pentagon (Algorithm) by Wkbj79

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Cross-references: square, edges, opposite, plane, onto, pentahedron, projection, golden number, ratio, side, length, diagonals, angles, inner, regular, polygon, planar
There are 18 references to this entry.

This is version 4 of pentagon, born on 2002-01-05, modified 2007-07-26.
Object id is 1397, canonical name is Pentagon.
Accessed 6052 times total.

Classification:

AMS MSC:

51-00 (Geometry :: General reference works )

Pending Errata and Addenda

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