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Wallace-Bolyai-Gerwein Theorem

Two Polygons are congruent by Dissection Iff they have the same Area. In particular, any Polygon is congruent by Dissection to a Square of the same Area. Laczkovich (1988) also proved that a Circle is congruent by Dissection to a Square (furthermore, the Dissection can be accomplished using Translations only).

See also Dissection


Klee, V. and Wagon, S. Old and New Unsolved Problems in Plane Geometry and Number Theory. Washington, DC: Math. Assoc. Amer., pp. 50-51, 1991.

Laczkovich, M. ``Von Neumann's Paradox with Translation.'' Fund. Math. 131, 1-12, 1988.

© 1996-9 Eric W. Weisstein