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.


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


square; dissection; five
Full Text: DOI


[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
[5] Maltby, S. J., Trisecting a rectangle, J. Combin. Theory, Ser. A, 66, 40-52 (1994) · Zbl 0797.05030
[6] Monsky, P., Dissecting a square into triangles, Amer. Math. Monthly, 77, 2, 161-164 (1970) · Zbl 0187.19701
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