# Difference between revisions of "Pentagon"

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==The Golden Ratio and the Pentagram== | ==The Golden Ratio and the Pentagram== | ||

− | The pentagon is closely associated with the | + | The pentagon is closely associated with the [[Golden Ratio]]. More specifically, the ratio of a diagonal to an edge is <math>\frac{1+\sqrt{5}}{2}</math>. By drawing each of the diagonals, one can form a pentagram, or five-pointed star, in which each of the internal angles is <math>36^{\circ}</math>.\\ |

− | By drawing each of the diagonals, one can form a pentagram, or five-pointed star, in which each of the internal angles is <math>36^{\circ}</math>.\\ | ||

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== See Also == | == See Also == | ||

*[[Polygon]] | *[[Polygon]] | ||

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{{stub}} | {{stub}} |

## Latest revision as of 19:39, 20 July 2016

In geometry, a **pentagon** is a polygon with 5 sides. Each angle of a regular pentagon is . The sum of the internal angles of any pentagon is .

## Construction

It is possible to construct a regular pentagon with compass and straightedge:

- Draw circle (red).
- Draw diameter and construct a perpendicular radius through .
- Construct the midpoint of , and label it .
- Draw (green).
- Construct the angle bisector of , and label its intersection with as (pink).
- Construct a perpendicular to at .
- Adjust your compass to length , and mark off points , and on circle .
- is a regular pentagon.

## The Golden Ratio and the Pentagram

The pentagon is closely associated with the Golden Ratio. More specifically, the ratio of a diagonal to an edge is . By drawing each of the diagonals, one can form a pentagram, or five-pointed star, in which each of the internal angles is .\\

## See Also

*This article is a stub. Help us out by expanding it.*