A problem of Sallee on equidecomposable convex bodies
HTML articles powered by AMS MathViewer
- by R. J. Gardner
- Proc. Amer. Math. Soc. 94 (1985), 329-332
- DOI: https://doi.org/10.1090/S0002-9939-1985-0784187-9
- PDF | Request permission
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
- S. Banach and A. Tarski, Sur la décomposition des ensembles de points en parties respectivement congruentes, Fund. Math. 6 (1924), 244-277.
- Lester Dubins, Morris W. Hirsch, and Jack Karush, Scissor congruence, Israel J. Math. 1 (1963), 239–247. MR 165424, DOI 10.1007/BF02759727
- G. T. Sallee, Research Problems: Are Equidecomposable Plane Convex Sets Convex Equidecomposable?, Amer. Math. Monthly 76 (1969), no. 8, 926–927. MR 1535587, DOI 10.2307/2317952
- 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, DOI 10.1017/CBO9780511609596
Bibliographic Information
- © Copyright 1985 American Mathematical Society
- 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