Smale (1958) 证明了在数学上可以将一个球体由内向外翻转，而不会在任何点引入尖锐的褶皱。这意味着存在一个从二维球面在欧几里得三维空间中的标准嵌入到镜像反射嵌入的正则同伦，使得在同伦的每个阶段，球体都被浸入在欧几里得空间中。这个结果非常违反直觉，并且证明非常技术性，以至于这个结果多年来都存在争议。
1961年，Arnold Shapiro 设计了一个显式的外翻方法，但没有公开。Phillips (1966) 听说了这个结果，并在尝试重现它的过程中，实际上设计了一种独立的自身方法。Morin 又设计了另一种外翻方法，这成为了 Max (1977) 电影的基础。Morin 的外翻方法还产生了描述该过程的显式代数方程。Shapiro 最初的方法随后由 Francis 和 Morin (1979) 发表。
电视剧犯罪剧集数字追凶第一季剧集 "狙击手零" (2005) 提到了球面外翻。
参见
外翻,
球体
通过 Wolfram|Alpha 探索
参考文献
Apéry, F. "An Algebraic Halfway Model for the Eversion of the Sphere." Tôhoku Math. J. 44, 103-150, 1992.Apéry, F.; and Franzoni, G. "The Eversion of the Sphere: a Material Model of the Central Phase." Rendiconti Sem. Fac. Sc. Univ. Cagliari 69, 1-18, 1999.Bulatov, V. "Sphere Eversion--Visualization of the Famous Topological Procedure." http://www.physics.orst.edu/~bulatov/vrml/evert.wrl.Francis, G. K. Ch. 6 in A Topological Picturebook. New York: Springer-Verlag, 1987.Francis, G. K. and Morin, B. "Arnold Shapiro's Eversion of the Sphere." Math. Intell. 2, 200-203, 1979.Levy, S. "A Brief History of Sphere Eversions." http://www.geom.umn.edu/docs/outreach/oi/history.html.Levy, S.; Maxwell, D.; and Munzner, T. Making Waves: A Guide to the Ideas Behind Outside In. Wellesley, MA: A K Peters, 1995. Book and 22 minute Outside-In. videotape. http://www.geom.umn.edu/docs/outreach/oi/.Max, N. "Turning a Sphere Inside Out." Videotape. Chicago, IL: International Film Bureau, 1977.Peterson, I. "Inside Moves." Sci. News 135, 299, May 13, 1989.Peterson, I. Islands of Truth: A Mathematical Mystery Cruise. New York: W. H. Freeman, pp. 240-244, 1990.Peterson, I. "Forging Links Between Mathematics and Art." Science News 141, 404-405, June 20, 1992.Phillips, A. "Turning a Surface Inside Out." Sci. Amer. 214, 112-120, Jan. 1966.Schimmrigk, R. http://www.th.physik.uni-bonn.de/th/People/netah/cy/movies/sphere.mpg.Smale, S. "A Classification of Immersions of the Two-Sphere." Trans. Amer. Math. Soc. 90, 281-290, 1958.Toth, G. Finite Möbius Groups, Minimal Immersion of Spheres, and Moduli. Berlin: Springer-Verlag, 2002.Trott, M. The Mathematica GuideBook for Symbolics. New York: Springer-Verlag, pp. 38-39, 2006. http://www.mathematicaguidebooks.org/.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, 1991.在 Wolfram|Alpha 上被引用
球面外翻
请引用本文
Weisstein, Eric W. "球面外翻。" 出自 MathWorld--Wolfram Web 资源。 https://mathworld.net.cn/SphereEversion.html
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