Carlyle circle

Another method of construction uses Carlyle circles, as shown below.

There is a procedure involving Carlyle circles for the construction of a regular 65537-gon.

There is a similar method involving Carlyle circles to construct regular heptadecagons.

Carlyle circles have been used to develop ruler-and-compass constructions of regular polygons.

In mathematics, a Carlyle circle is a certain circle in a coordinate plane associated with a quadratic equation.

To construct a regular 257-gon using Carlyle circles, as many as 24 Carlyle circles are to be constructed.

See main article: Carlyle circle The Carlyle circle was invented as a geometric method to find the roots of a quadratic equation.

A certain construction of the regular heptadecagon involving the Carlyle circles can be represented by the expression 8R + 4R + 22C + 11C and has simplicity 45.