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28 March 2024
 
  » arxiv » 2001.3289

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Dissecting a square into congruent polygons
Hui Rao ; Lei Ren ; Yang Wang ;
Date Fri, 10 Jan 2020 02:45:47 GMT (1807kb)
AbstractWe study the dissection of a square into congruent convex polygons with $q$-vertices. Yuan emph{et al.} [Dissection the square into five congruent parts, Discrete Math. extbf{339} (2016) 288-298] posed the question that if the number of tiles is a prime number $geq 3$, is it true that the polygon must be a rectangle. We conjecture that the same conclusion still holds even if the number of tiles is an odd number $geq 3$. Our conjecture has been confirmed for triangles in earlier works. We prove that the conjecture holds if either the prototile is a convex $q$-gon with $qgeq 6$ or it is a right-angle trapezoid.
Source arXiv, 2001.3289
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