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 there exist a triangle and its image under a homothety with ratio such that . We prove the conjecture of Grünbaum that if is centrally symmetric, then can be chosen so that their centroids coincide with the center of .

**[1]**Edgar Asplund,*Comparison between plane symmetric convex bodies and parallelograms.*, Math. Scand.**8**(1960), 171–180. MR**0125495****[2]**A. S. Besicovitch,*Measure of asymmetry of convex curves*, J. London Math. Soc.**23**(1948), 237–240. MR**0027543****[3]**H. G. Eggleston,*Convexity*, Cambridge Tracts in Mathematics and Mathematical Physics, No. 47, Cambridge University Press, New York, 1958. MR**0124813****[4]**Branko Grünbaum,*Measures of symmetry for convex sets*, Proc. Sympos. Pure Math., Vol. VII, Amer. Math. Soc., Providence, R.I., 1963, pp. 233–270. MR**0156259****[5]**Marek Lassak,*Approximation of plane convex bodies by centrally symmetric bodies*, J. London Math. Soc. (2)**40**(1989), no. 2, 369–377. MR**1044283**, 10.1112/jlms/s2-40.2.369

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DOI:
https://doi.org/10.1090/S0002-9939-1992-1057956-1

Article copyright:
© Copyright 1992
American Mathematical Society