# zbMATH — the first resource for mathematics

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:
##### References:
 [1] Archimedes, Ostomachion. [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 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 [7] W. Moser, Research Problems in Discrete Geometry, Montreal, 1981, Problem 34. · Zbl 0528.52001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.