| 单词 | Wallace-Bolyai-Gerwein Theorem |
| 释义 | Wallace-Bolyai-Gerwein TheoremTwo Polygons are congruent by Dissection Iff they have the same Area. Inparticular, 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, theDissection 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. |
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