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math.MG2026
Tiling a triangle into a prime number of congruent triangles
Michael Beeson
We show that, apart from a few known exceptions, if a triangle is cut into congruent triangles, then is not a prime number. The exceptions are cutting an isosceles triangle…
math.CO2026
Solution of Erdős Problem 633
Michael Beeson, Miklos Laczkovich, Yan X. Zhang
We classify triangles that can be tiled only into a square number of congruent triangles, settling Erdős Problem 633.
math.CO2026
Rationality of certain triangle tilings
Michael Beeson, Yan X Zhang
We consider tilings of a triangle by congruent copies of a triangle that has one angle equal to , has non-commensurable angles (that is, not all angles are rationa…