Heilbronn Problem for Six Points in a Planar Convex Body
For any six points in a planar convex body K there must be at least one triangle, formed by three of these points, with area not greater than 1/6 of the area of K. This upper bound 1/6 is best possible.
KeywordsConvex Hull London Math Global Maximum Compact Region Unique Critical Point
Unable to display preview. Download preview PDF.
- 5.Moser, W. & Pach,J., “100 Research Problem in Discrete Geometry”, MacGill University, Montreal, Que. 1986.Google Scholar
- 8.Roth, K.F., On a problem of Heilbronn III, Proc. London Math. Soc., 25 (1974), 543–549.Google Scholar
- 9.Roth, K.F., Estimation of the area of the smallest triangle obtained by selecting three out of n points in a disc of unit area, Amer. Math. Soc. Proc. Symp. Pure Math., 24: 251–262, 1973.Google Scholar
- 12.Yang Lu & Zhang Jingzhong, The problem of 6 points in a square, in “Lectures in Math. (2)”, 151–175, Sichuan People’s Publishing House 1980, pp. 151–175. (in Chinese).Google Scholar
- 13.Yang Lu & Zhang Jingzhong, A conjecture concerning six points in a square, in “Mathematical Olympiad in China”, Hunan Education Publishing House 1990.Google Scholar
- 16.Yang Lu, Zhang Jingzhong & Zeng Zhenbing, Heilbronn problem for five points, Preprint, International Centre for Theoretical Physics, 1991, IC/91/252.Google Scholar
- 17.Yang Lu, Zhang Jingzhong & Zeng Zhenbing, On Goldberg’s conjecture: computing the first several Heilbronn numbers, Preprint, Universitat Bielefeld, 1991, ZiF–Nr.91/29, SFB-Nr.91/074.Google Scholar
- 18.Yang Lu, Zhang Jingzhong & Zeng Zhenbing, Searching dependency between algebraic equations: an algorithm applied to automated reasoning, Preprint, International Centre for Theoretical Physics, 1991, IC/91/6.Google Scholar