Cutting a triangle into equal triangles

TL;DR

This paper proves that almost every triangle can be uniquely dissected into n^2 equal triangles, using advanced mathematical tools from linear algebra, calculus, and measure theory.

Contribution

It establishes the existence and uniqueness of such dissections for almost all triangles, providing a comprehensive mathematical framework.

Findings

Almost every triangle admits a unique n^2 equal triangle dissection.

The dissection process relies on linear algebra, calculus, and measure theory.

The dissection is unique for each n.

Abstract

We prove that almost every triangle can be dissected only into $n^2$ triangles which have to be equal one another. Moreover, such a dissection is unique for every $n$. It turns out that to solve this "simple" problem it is convenient to use some tools from linear algebra, calculus and measure theory.