On equidissection of balanced polygons
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In this paper, we show that a lattice balanced polygon of odd area be cut into an odd number of triangles of equal areas. The 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 between the equidissection problem and tropical geometry. Bibliography: 9 titles.
KeywordsStein Equal Area Tropical Geometry Balance Polygon
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