Approximation of Convex Bodies by Rhombi and by other Axially Symmetric Bodies

Marek Lassak
Institut für Informatik
Freie Universität Berlin
Takustr. 9, D-14195 Berlin

Report B 99-22
December 1999

Abstract: Let C be an arbitrary planar convex body. We prove that C contains an axially symmetric convex body of area at least 2/3 | C |. Also approximation by some specific axially symmetric bodies is considered. In particular, we can inscribe a rhombus of area at least ½ | C | in C, and we can circumscribe a homothetic rhombus of area at most 2 | C | about C. The homothetic ratio is at most 2. Those coefficients ½ and 2 and also the homothetic ratio 2 cannot be improved.

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