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'pentagon'
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| Title of object: |
pentagon |
| Canonical Name: |
Pentagon |
| Type: |
Definition |
| Created on: |
2002-01-05 22:51:13 |
| Modified on: |
2007-07-26 01:11:07 |
| Classification: |
msc:51-00 |
Revision comment (for changes between this and next version):
| Changes for correction #12773 ('add a word'). |
Preamble:
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{xypic}
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Content:
A \emph{pentagon} is a 5-sided 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. |
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