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.
(red).
and construct a perpendicular radius through 
, and label it 
.
(green).
, and label its intersection with 
(pink).
, 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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