Borsuk 猜想认为，可以将一个广义直径为 1 的 
维形状切割成 
块，每块的直径都小于原始形状的直径。对于 
、3 以及当边界“光滑”时，这个猜想是成立的。然而，所需的最小块数已被证明会随着 
的增加而增加。由于当 
时 
，该猜想在高维度下变为错误。
Kahn 和 Kalai (1993) 在 1326 维中找到了一个反例，Nilli (1994) 在 946 维中找到了一个反例。Hinrichs 和 Richter (2003) 表明，对于所有 
，该猜想都是错误的。
Borsuk 猜想
另请参阅
广义直径, Keller 猜想, Lebesgue 最小问题使用 Wolfram|Alpha 探索
参考文献
Borsuk, K. "Über die Zerlegung einer Euklidischen
-dimensionalen Vollkugel in 
Mengen." Verh. Internat. Math.-Kongr. Zürich 2, 192, 1932.Borsuk, K. "Drei Sätze über die 
-dimensionale euklidische Sphäre." Fund. Math. 20, 177-190, 1933.Cipra, B. "If You Can't See It, Don't Believe It...." Science 259, 26-27, 1993.Cipra, B. What's Happening in the Mathematical Sciences, Vol. 1. Providence, RI: Amer. Math. Soc., pp. 21-25, 1993.Grünbaum, B. "Borsuk's Problem and Related Questions." In Convexity: Proceedings of the Seventh Symposium in Pure Mathematics of the American Mathematical Society, Held at the University of Washington, Seattle, June 13-15, 1961. Providence, RI: Amer. Math. Soc., pp. 271-284, 1963.Hinrichs, A. and Richter, C. "New Sets with Large Borsuk Numbers." Disc. Math. 270, 137-147, 2003.Kahn, J. and Kalai, J. K. G. "A Counterexample to Borsuk's Conjecture." Bull. Amer. Math. Soc. 29, 60-62, 1993.Lyusternik, L. and Schnirel'mann, L. Topological Methods in Variational Problems. Moscow, 1930.Lyusternik, L. and Schnirel'mann, L. "Topological Methods in Variational Problems and Their Application to the Differential Geometry of Surfaces." Uspehi Matem. Nauk (N.S.) 2, 166-217, 1947.Nilli, A. "On Borsuk's Problem." Jerusalem Combinatorics '93. Papers from the International Conference on Combinatorics held in Jerusalem, May 9-17, 1993 (Ed. H. Barcelo and G. Kalai.) Providence, RI: Amer. Math. Soc., pp. 209-210, 1994.
引用此页
Eric Weisstein. "Borsuk 猜想。" 来自 MathWorld--Wolfram Web 资源。 https://mathworld.net.cn/BorsuksConjecture.html