Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 52A10, 52A15

Retrieve articles in all journals with MSC: 52A10, 52A15

Additional Information

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

American Mathematical Society