Experimental Statistics for Mirzakhani’s Theorem

Abstract

In her seminal 2008 article, Maryam Mirzakhani showed that the ratio that two topological types of curves occur in is a rational number. In this article, we describe the process by which we obtained experimental evidence that separating and non-separating curves on the surface of genus two occur in the ratio $1:48$.¹

Keywords:

• Mapping class group
• Mirzakhani
• topological types of curves

Declaration of Interest

No potential conflict of interest was reported by the author(s).

Notes

1 markcbell.github.io