Constructing a Regular Heptagon Using Lill's Method

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

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

This Demonstration shows how to construct a regular heptagon using Lill's method for solving cubic equations.


The points of a regular heptagon with vertices on a circle of radius 1 are given by . Since is a solution, if we divide the polynomial by , we get


If , then



leads to the cubic equation


It has solutions , , .

This follows from the trigonometric identity


Set and to get


which factors as


There are solutions when the points and coincide.


Contributed by: Izidor Hafner (September 2017)
Open content licensed under CC BY-NC-SA




[1] G. E. Martin, Geometric Constructions, New York: Springer, 1998 p. 45.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.