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).

**References**

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

1999-05-26