Difference between revisions of "Pentagon"
Jbatterson (talk | contribs) (→The Golden Ratio) |
|||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 14: | Line 14: | ||
# <math>AGHIJ</math> is a regular pentagon. | # <math>AGHIJ</math> is a regular pentagon. | ||
| − | ==The Golden Ratio | + | ==The Golden Ratio== |
| − | 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>. |
| − | |||
== See Also == | == See Also == | ||
Latest revision as of 08:59, 6 June 2022
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
The pentagon is closely associated with the Golden Ratio. More specifically, the ratio of a diagonal to an edge is 
.
See Also
This article is a stub. Help us out by expanding it.
