# Constructing a Regular Heptagon Using Gleason's Method

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

This Demonstration shows Gleason's method for constructing a regular heptagon, using the following steps:

[more]
Contributed by: Izidor Hafner (September 2017)

Open content licensed under CC BY-NC-SA

## Snapshots

## 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.

## Permanent Citation

"Constructing a Regular Heptagon Using Gleason's Method"

http://demonstrations.wolfram.com/ConstructingARegularHeptagonUsingGleasonsMethod/

Wolfram Demonstrations Project

Published: September 15 2017