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Proceedings of the American Mathematical Society

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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
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?)

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  • [3] G. T. Sallee, Research Problems: Are Equidecomposable Plane Convex Sets Convex Equidecomposable?, Amer. Math. Monthly 76 (1969), no. 8, 926–927. MR 1535587, 10.2307/2317952
  • [4] Stan Wagon, The Banach-Tarski paradox, Encyclopedia of Mathematics and its Applications, vol. 24, Cambridge University Press, Cambridge, 1985. With a foreword by Jan Mycielski. MR 803509

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Keywords: Convex body, equidecomposable, scissors equidecomposable, convex equidecomposable
Article copyright: © Copyright 1985 American Mathematical Society