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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) | Abstract: | We 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 | Services: | Forum | Review | PDF | Favorites |
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