Hydrostatic-Based Proofs in Geometry

TL;DR

This paper introduces a hydrostatic approach to classical geometry problems, demonstrating how fluid statics principles can provide new insights and proofs for geometric identities involving polygons.

Contribution

It presents a novel method applying fluid statics to derive geometric results, bridging physical principles with mathematical proofs.

Findings

Derived two new geometric results using hydrostatic principles

Illustrated the utility of physical intuition in mathematical proofs

Connected fluid mechanics concepts with classical geometry

Abstract

Inspired by Tokieda's work on mechanical insights in geometry, we explore a hydrostatic approach to classical geometric problems. Using principles of fluid statics, we derive two mathematical results regarding polygons. These results illustrate how physical principles can assist in understanding mathematical identities.