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A problem of Sallee on equidecomposable convex bodies


Author: R. J. Gardner
Journal: Proc. Amer. Math. Soc. 94 (1985), 329-332
MSC: Primary 52A10; Secondary 52A15
DOI: https://doi.org/10.1090/S0002-9939-1985-0784187-9
MathSciNet review: 784187
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Abstract: We show that equidecomposable planar convex bodies need not be convex equidecomposable. This answers a question of Sallee. We also show that convex and scissors equidecomposability are equivalent notions for convex bodies in the plane, and include a discussion of these concepts in higher dimensions.


References [Enhancements On Off] (What's this?)

  • [1] S. Banach and A. Tarski, Sur la décomposition des ensembles de points en parties respectivement congruentes, Fund. Math. 6 (1924), 244-277.
  • [2] L. Dubins, M. Hirsch and J. Karush, Scissor congruence, Israel J. Math. 1 (1963), 239-247. MR 0165424 (29:2706)
  • [3] G. T. Sallee, Are equidecomposable plane convex sets convex equidecomposable? Amer. Math. Monthly 76 (1979), 926-927. MR 1535587
  • [4] S. Wagon, The Banach-Tarski paradox, Cambridge Univ. Press, New York, 1985. MR 803509 (87e:04007)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0784187-9
Keywords: Convex body, equidecomposable, scissors equidecomposable, convex equidecomposable
Article copyright: © Copyright 1985 American Mathematical Society

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