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Dissecting the square into five congruent parts. (English) Zbl 1322.05038

Summary: We give an affirmative answer to an old conjecture proposed by Ludwig Danzer: there is a unique dissection of the square into five congruent convex tiles.

MSC:

05B45 Combinatorial aspects of tessellation and tiling problems
52C20 Tilings in \(2\) dimensions (aspects of discrete geometry)

Keywords:

square; dissection; five
Full Text: DOI

References:

[2] Boros, E.; Füredi, Z., Rectangular dissections of a square, European J. Combin., 9, 2, 271-280 (1988) · Zbl 0642.05016
[3] Grünbaum, B.; Shephard, G. C., Tilings and Patterns (1990), W. H. Freeman: W. H. Freeman London · Zbl 0601.05001
[4] Häggkvist, R.; Lindberg, P.-O.; Lindström, B., Dissecting a square into rectangles of equal area, Discrete Math., 47, 321-323 (1983) · Zbl 0527.05022
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[6] Monsky, P., Dissecting a square into triangles, Amer. Math. Monthly, 77, 2, 161-164 (1970) · Zbl 0187.19701
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