Geometry in the Courtroom

TL;DR

This survey explores how pure mathematics, especially geometry and topology, has been applied in legal contexts, illustrating its role beyond traditional statistics in court cases and legal reasoning.

Contribution

It compiles diverse examples of geometric and topological applications in law, highlighting their educational value and real-world relevance.

Findings

Geometric concepts have been used in legal reasoning and court cases.

Examples include the Pythagorean theorem and the Ham Sandwich Theorem.

Geometry offers engaging real-world applications for math education.

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.