Difference between revisions of "Pentagon"
(→See also: cap) |
Jbatterson (talk | contribs) (→The Golden Ratio) |
||
(7 intermediate revisions by 5 users not shown) | |||
Line 13: | Line 13: | ||
# Adjust your compass to length <math>AG</math>, and mark off points <math>H</math>, <math>I</math> and <math>J</math> on circle <math>O</math>. | # Adjust your compass to length <math>AG</math>, and mark off points <math>H</math>, <math>I</math> and <math>J</math> on circle <math>O</math>. | ||
# <math>AGHIJ</math> is a regular pentagon. | # <math>AGHIJ</math> 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 <math>\frac{1+\sqrt{5}}{2}</math>. | ||
== See Also == | == See Also == |
Latest revision as of 09:59, 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.
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.