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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Approximation of convex bodies by triangles


Author: Marek Lassak
Journal: Proc. Amer. Math. Soc. 115 (1992), 207-210
MSC: Primary 52A10; Secondary 52A27
MathSciNet review: 1057956
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Abstract: We show that for every plane convex body $ C$ there exist a triangle $ {T_1}$ and its image $ {T_2}$ under a homothety with ratio $ \tfrac{5} {2}$ such that $ {T_1} \subset C \subset {T_2}$. We prove the conjecture of Grünbaum that if $ C$ is centrally symmetric, then $ {T_1},{T_2}$ can be chosen so that their centroids coincide with the center of $ C$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1057956-1
PII: S 0002-9939(1992)1057956-1
Article copyright: © Copyright 1992 American Mathematical Society