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On equidissection of balanced polygons

2012/06/20 by Daniil Rudenko, Rudenko, Daniil
Computer Science · Engineering · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #graph theory and CDMA systems #math.AG #math.CO

paper · pdf · doi:10.48550/arxiv.1206.4591

openalex publication_date 2012/06/20 · arxiv created 2012/08/03 · arxiv updated 2012/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we show that a lattice balanced polygon of odd area cannot be cut into an odd number of triangles of equal areas. First result of this type was obtained by Paul Monsky in 1970. He proved that a square cannot be cut into an odd number of triangles of equal areas. In 2000 Sherman Stein conjectured that the same holds for any balanced polygon. We also show connections between the equidissection problem and tropical geometry.

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