• Thumbnail for Sphere eversion
    differential topology, sphere eversion is the process of turning a sphere inside out in a three-dimensional space (the word eversion means "turning inside...
    12 KB (1,126 words) - 22:16, 30 June 2024
  • up eversion in Wiktionary, the free dictionary. Eversion (from the verb evert) is the process of turning inside-out. Eversion may refer to: Eversion (kinesiology)...
    902 bytes (156 words) - 19:25, 29 January 2023
  • In geometry, minimax eversions are a class of sphere eversions, constructed by using half-way models. It is a variational method, and consists of special...
    4 KB (521 words) - 20:34, 27 December 2022
  • Thumbnail for Sphere
    sphere inside out in a three-dimensional space with possible self-intersections but without creating any creases, in a process called sphere eversion...
    41 KB (5,327 words) - 20:13, 25 October 2024
  • Thumbnail for Bernard Morin
    group that first exhibited an eversion of the sphere, i.e., a homotopy which starts with a sphere and ends with the same sphere but turned inside-out. He...
    5 KB (356 words) - 08:24, 4 September 2024
  • Thumbnail for Morin surface
    half-way model of the sphere eversion discovered by Bernard Morin. It features fourfold rotational symmetry. If the original sphere to be everted has its...
    6 KB (781 words) - 02:46, 4 February 2022
  • Thumbnail for Manifold
    Manifold (section Sphere)
    Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, and also the Klein bottle and real projective plane. The...
    69 KB (9,645 words) - 11:16, 30 October 2024
  • Thumbnail for Homotopy principle
    (non-complete) Riemannian metric of positive (or negative) curvature. Sphere eversion without creasing or tearing can be done using C 1 {\displaystyle C^{1}}...
    11 KB (1,721 words) - 01:40, 6 January 2024
  • Thumbnail for Immersion (mathematics)
    ^{n}} ⁠ as the homotopy groups of a certain Stiefel manifold. The sphere eversion was a particularly striking consequence. Morris Hirsch generalized...
    23 KB (2,869 words) - 09:43, 3 September 2024
  • Thumbnail for Stephen Smale
    immersion of the sphere into three-dimensional space can be deformed (through immersions) into its negation, which is now known as sphere eversion. He also extended...
    23 KB (2,160 words) - 19:36, 22 May 2024
  • straight line intersecting the Nikodym set only in that point. Sphere eversion: A sphere can, topologically, be turned inside out. Abilene paradox: People...
    56 KB (7,846 words) - 15:14, 29 October 2024
  • fact that seven colors are necessary and sufficient on the doughnut. Sphere eversion is described in terms of two separate wormholes filling an apple. Reminding...
    13 KB (1,718 words) - 23:50, 4 May 2024
  • Thumbnail for Boy's surface
    pieces. Boy's surface can be used in sphere eversion, as a half-way model. A half-way model is an immersion of the sphere with the property that a rotation...
    11 KB (1,391 words) - 15:45, 31 October 2024
  • Thumbnail for Mathematical visualization
    diagonal surface demonstrates the 27 lines on a cubic surface. Sphere eversion – that a sphere can be turned inside out in 3 dimension if allowed to pass...
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  • ball theorem Poincaré–Hopf theorem Stokes' theorem De Rham cohomology Sphere eversion Frobenius theorem (differential topology) Distribution (differential...
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  • 1957 – Stephen Smale provides the existence proof for crease-free sphere eversion. 1958 – Alexander Grothendieck's proof of the Grothendieck–Riemann–Roch...
    64 KB (7,788 words) - 18:50, 24 September 2024
  • Thumbnail for Maps of manifolds
    A Morin surface, an immersion used in sphere eversion....
    5 KB (558 words) - 17:49, 29 January 2024
  • immersions of the projective plane, and deformations between them; sphere eversion and the Morin surface; group theory, the mapping class groups of surfaces...
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  • 2-sphere immersed in R 3 {\displaystyle \mathbb {R} ^{3}} . In particular, this means that sphere eversions exist, i.e. one can turn the 2-sphere "inside-out"...
    6 KB (862 words) - 03:51, 27 March 2024
  • space rendering of knot complements. [1] Outside In, a movie about sphere eversion. [2] The shape of space, exploring possible three dimensional spaces...
    6 KB (586 words) - 16:17, 29 September 2024
  • Thumbnail for Willmore energy
    Willmore energy is used in constructing a class of optimal sphere eversions, the minimax eversions. Willmore conjecture Bryant, Robert L. (1984), "A duality...
    5 KB (691 words) - 23:02, 4 October 2024
  • 2017 film Outside In, a 1994 computer-generated film demonstrating sphere eversion created by the Geometry Center Outside In (book), a 2020 picture book...
    626 bytes (106 words) - 11:14, 27 March 2024
  • Newton, Massachusetts) was an American mathematician known for his eversion of the sphere and Shapiro's lemma. He also was the author of an article on Clifford...
    4 KB (561 words) - 15:57, 24 June 2024
  • of California, (retrieved July 27, 2012). "A History of Sphere Eversions" – Turning a sphere inside out, (retrieved July 27, 2012). Brief History of the...
    111 KB (13,486 words) - 21:29, 15 August 2024
  • (disambiguation) Sexual inversion (disambiguation) Involution (disambiguation) Eversion (disambiguation) Reversal (disambiguation) This disambiguation page lists...
    4 KB (582 words) - 20:54, 10 June 2024
  • man. Themes explored include the ubiquity of locative technology, the eversion of cyberspace and the political climate of the United States in the aftermath...
    47 KB (5,012 words) - 03:36, 27 September 2024
  • Thumbnail for Penile-vaginal intercourse
    "Vaginal length and sexual function after colpopexy for complete uterovaginal eversion". American Journal of Obstetrics and Gynecology. 169 (2): 284–288. doi:10...
    45 KB (5,143 words) - 01:50, 16 October 2024
  • one-dimensional case of the mean curvature flow Willmore flow, as in minimax eversions of spheres Inverse mean curvature flow Intrinsic geometric flows are flows on...
    4 KB (539 words) - 01:41, 30 September 2024
  • Entertainment Sony Online Entertainment, Gamania, Akella, Square Enix, Ubisoft Eversion 2010 Zaratustra Productions Zaratustra Productions Everyday Shooter 2007...
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  • becomes moderately famous for a while during the period after the sky eversion. Cornell signs up for a pharmaceutical testing program to earn some money...
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