No triangle can be cut into seven congruent triangles

2018/11/23 by Michael Beeson, Beeson, Michael · 2 citations
Computer Science · Mathematics · #51M20 (primary) 51M04 (secondary) #FOS: Mathematics #History and Overview (math.HO) #History and Theory of Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1811.09723

openalex publication_date 2018/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the theorem in the title, and prove the theorem for 11 as well as 7. By previous work of others, the problem reduces to a number of cases. The cases not solved already are solved here.

Citations

• Tilings of an Isosceles Triangle

Cited by

• Tiling a triangle into a prime number of congruent triangles
• Tiling an Equilateral Triangle

Related

• No Prime Tiling of an Isosceles Triangle
• Dissecting Equilateral Triangles into Non-Congruent Equilateral Triangles: A Novel Proof of Tutte's Result
• Cutting a triangle into equal triangles
• Tiling a triangle into a prime number of congruent triangles
• Congruent number triangles with the same hypotenuse