## The Heptagon, Hyperbola and Lill’s Circle

The heptagon cannot be constructed with just a ruler and a compass. However, in this post I’ll show how you can construct the heptagon using a hyperbola and the Lill’s circle of a third degree polynomial. The heptagon construction is very similar in nature to my trisection construction that I presented in my “Trisection Hyperbolas… Continue reading The Heptagon, Hyperbola and Lill’s Circle

## Trisection Hyperbolas and Lill’s Circle

In my previous blog post about trisection “Angle Trisection: a Neusis Construction using Lill’s Method and Lill’s Circle”, I showed a “mechanical” method for trisecting an angle smaller than 90 degrees. The neusis construction involved the Lill’s method representation of cubic equations of the form x3  -3tan(θ)x2 -3x + tan(θ). These cubic equations have 3 real… Continue reading Trisection Hyperbolas and Lill’s Circle

## Angle Trisection: a Neusis Construction using Lill’s Method and Lill’s Circle

The problem of trisecting an angle using just a compass and a straightedge is an impossible problem. However, the problem of angle trisection can be solved if we are allowed the use of a marked ruler. Geometric constructions that use a marked ruler are called neusis constructions. You can learn more about the topic of… Continue reading Angle Trisection: a Neusis Construction using Lill’s Method and Lill’s Circle