Tilings of convex polygons by equilateral triangles of many different\n sizes

2019/03/25 by Christian Richter, Richter, Christian
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #Mathematics and Applications #Cellular Automata and Applications

paper · pdf · doi:10.48550/arxiv.1903.10431

Abstract

An equilateral triangle cannot be dissected into finitely many mutually\nincongruent equilateral triangles [Tutte 1948]. Therefore Tuza [Tuza 1991]\nasked for the largest number s=s(n) such that there is a tiling of an\nequilateral triangle by n equilateral triangles of s(n) different sizes. We\nsolve that problem completely and consider the analogous questions for\ndissections of convex k-gons into equilateral triangles, k=4,5,6. Moreover,\nwe discuss all these questions for the subclass of tilings such that no two\ntiles are translates of each other.\n

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