On Dividing a Rectangle

TL;DR

This paper provides a new elementary proof demonstrating that an arbitrary rectangle cannot be divided into three congruent, non-rectangular regions, addressing a historical geometric problem.

Contribution

It introduces a novel elementary proof confirming the impossibility of dissecting a rectangle into three congruent, non-rectangular parts, resolving a longstanding question.

Findings

Proves the impossibility of dividing a rectangle into 3 congruent, non-rectangular regions

Provides a new elementary proof of this geometric fact

Addresses a historical problem in geometric dissections

Abstract

This paper deals with the history of the following problem: "Can an arbitrary rectangle be dissected into 3 non-rectangular congruent regions?" We present a new elementary proof that the answer is indeed no.