“Heilbronn Triangle Problem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Heilbronn Triangle Problem

释义

Heilbronn Triangle Problem

N.B. A detailed on-line essay by S. Finchwas the starting point for this entry.

Given any arrangement of points within a Unit Square, let be the smallest value for whichthere is at least one Triangle formed from three of the points with Area . The first fewvalues are

Komlós et al. (1981, 1982) have shown that there are constants

such that

for any

and all sufficiently large

Using an Equilateral Triangle of unit Area instead gives the constants

References

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/hlb/hlb.html

Goldberg, M. ``Maximizing the Smallest Triangle Made by Points in a Square.'' Math. Mag. 45, 135-144, 1972.

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 242-244, 1994.

Komlos, J.; Pintz, J.; and Szemerédi, E. ``On Heilbronn's Triangle Problem.'' J. London Math. Soc. 24, 385-396, 1981.

Komlos, J.; Pintz, J.; and Szemerédi, E. ``A Lower Bound for Heilbronn's Triangle Problem.'' J. London Math. Soc. 25, 13-24, 1982.

Roth, K. F. ``Developments in Heilbronn's Triangle Problem.'' Adv. Math. 22, 364-385, 1976.

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