Constructing a Regular Heptagon Using Gleason's Method
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This Demonstration shows Gleason's method for constructing a regular heptagon, using the following steps:
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Contributed by: Izidor Hafner (September 2017)
Open content licensed under CC BY-NC-SA
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Details
The points of a regular heptagon inscribed in the circle of radius 1 are given by . Since is a solution, divide the polynomial by to get
.
If
then
.
Substitute to get the third-degree equation
with solutions
,
,
.
These solutions also follow from the trigonometric identity
.
Set and to get
,
which factors as
.
Reference
[1] G. E. Martin, Geometric Constructions, New York: Springer, 1998 p. 45.
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