Geometry in the Courtroom

Abstract

There has been a recent media blitz on a cohort of mathematicians valiantly working to fix America's democratic system by combatting gerrymandering with geometry. While statistics commonly features in the courtroom (forensics, DNA analysis, etc.), the gerrymandering news raises a natural question: in what other ways has pure math, specifically geometry and topology, been involved in court cases and legal scholarship? In this survey article, we collect a few examples with topics ranging from the Pythagorean formula to the Ham Sandwich Theorem, and we discuss some jurists' perspectives on geometric reasoning in the legal realm. One of our goals is to provide math educators with engaging real-world instances of some abstract geometric concepts.