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arXiv · 2607.23453

Tiling a triangle into a prime number of congruent triangles

Michael Beeson
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Abstract

We show that, apart from a few known exceptions, if a triangle is cut into $N$ congruent triangles, then $N$ is not a prime number. The exceptions are cutting an isosceles triangle in half, cutting an equilateral triangle in three, a 3-tiling of a 30-60-90 triangle, and the long-known biquadratic tilings of a certain right triangle, when $N$ is a sum of two squares.

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Michael Beeson. 2026-07-26. Tiling a triangle into a prime number of congruent triangles. https://arxiv.org/abs/2607.23453

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