Approximation of convex bodies by triangles

Lassak, Marek

doi:10.1090/S0002-9939-1992-1057956-1

Approximation of convex bodies by triangles
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Proc. Amer. Math. Soc. 115 (1992), 207-210 Request permission

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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