Dissecting Equilateral Triangles into Non-Congruent Equilateral Triangles: A Novel Proof of Tutte's Result

TL;DR

This paper proves that an equilateral triangle cannot be subdivided into finitely many smaller non-congruent equilateral triangles sharing only one vertex, using a novel proof that avoids electrical network methods.

Contribution

It provides a new proof of Tutte's result on the impossibility of dissecting an equilateral triangle into finitely many non-congruent equilateral triangles sharing only one vertex, without electrical network techniques.

Findings

Proves the impossibility of such dissections.

Introduces a novel proof technique avoiding electrical networks.

Confirms Tutte's classical result with a new approach.

Abstract

In this paper, we show that an equilateral triangle cannot be dissected into finitely many smaller equilateral triangles, no two of which share two vertices. We do this without the use of Electrical Networks.