Difference between revisions of "Pentagon"
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− | In [[geometry]], a '''pentagon''' is a [[polygon]] with 5 sides. | + | In [[geometry]], a '''pentagon''' is a [[polygon]] with 5 sides. Each [[angle]] of a [[regular polygon | regular]] pentagon is <math>108^{\circ}</math>. The sum of the internal angles of any pentagon is <math>540^{\circ}</math>. |
== Construction == | == Construction == | ||
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==The Golden Ratio and the Pentagram== | ==The Golden Ratio and the Pentagram== | ||
− | 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>.\ |
== See Also == | == See Also == |
Revision as of 19:38, 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
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