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

# Category: Lill’s method

## 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

## Lill’s method and the Philo Line for Right Angles

(Note: This is an article from 2016 that I posted on Hubpages. In this article I used Riaz’s way of illustrating Lill’s method. To become more familiar with Lill’s method I recommend going through the links provided in my Lill’s Method page. Also see my Papers page and my Lill’s method articles/posts. ) In this… Continue reading Lill’s method and the Philo Line for Right Angles

## Lill’s Method and Geometric Solutions to Quadratic Equations With Complex Roots

I already wrote a paper called “Lill’s Method and Graphical Solutions to Quadratic Equations” that shows how to solve quadratic equations using Lill’s method. In this post I want to show an alternative way of solving quadratic equations that have complex or imaginary roots. This method was briefly mentioned in the paper “Geometric Solution of… Continue reading Lill’s Method and Geometric Solutions to Quadratic Equations With Complex Roots