# Morley's Trisector Theorem

## Date of Graduation

Summer 2005

## Degree

Master of Science in Mathematics

## Department

Mathematics

## Committee Chair

Kishor Shah

## Abstract

The turn of the twentieth century, mathematician Frank Morley discovered that the adjacent angle trisectors of any triangle will intersect to form the vertices of an equilateral triangle. For the next one hundred years mathematicians have proved and reproved this intriguing theorem called Morley’s Trisector Theorem. In our thesis, we will explain five different types of approaches taken by mathematicians to prove this theorem. The five types of proofs we closely study are the direct proof by A. Letac, the indirect proof by John Conway and also by James Smart, the proof using complex variables by Clarence Lubin, the proof using group theory by Fields medalist Alain Connes, and the complete solution by W.J. Dobbs.

## Keywords

plane geometry, Morley triangle, equilateral triangle, angle trisector, complex plane

## Subject Categories

Mathematics

## Copyright

© Carolyn H. Shand-Hawkins

## Recommended Citation

Shand-Hawkins, Carolyn H., "Morley's Trisector Theorem" (2005). *MSU Graduate Theses*. 1618.

https://bearworks.missouristate.edu/theses/1618

**Dissertation/Thesis**