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- ...dies (which is the same for all observers) and the rate of rotation of the spheres (which is different for observers with differing rates of rotation). Only f In the 1846 Andrew Motte translation of Newton's words:<ref name=spheres>See the ''Principia'' on line at <!-- Dead link at 2010-05-13 -- [https:// ...24 KB (3,786 words) - 13:54, 21 November 2024
- ...n [[sphere]] in terms of the <math>L^2</math> norm of this function on two spheres, one with bigger radius and one with smaller radius. == Statement of the three spheres inequality == ...1 KB (203 words) - 09:19, 5 February 2024
- In [[mathematics]], the '''walk-on-spheres method (WoS)''' is a numerical probabilistic [[algorithm]], or [[Monte-Carl by sampling only the exit-points out of successive spheres, rather than simulating in detail the path of the process. This often makes ...15 KB (2,249 words) - 03:37, 27 August 2023
- '''Chern's conjecture for hypersurfaces in spheres''', unsolved as of 2018, is a conjecture proposed by Chern in the field of This became known as the '''Chern's conjecture for minimal hypersurfaces in spheres''' (or '''Chern's conjecture for minimal hypersurfaces in a sphere''') ...11 KB (1,664 words) - 17:27, 28 June 2024
Page text matches
- ...[[packing problem]] with the objective of packing a given number of equal spheres inside a [[unit sphere]]. It is the three-dimensional equivalent of the [[c ! rowspan=2 | Number of<br>inner spheres ...3 KB (324 words) - 01:34, 21 June 2024
- ...n [[sphere]] in terms of the <math>L^2</math> norm of this function on two spheres, one with bigger radius and one with smaller radius. == Statement of the three spheres inequality == ...1 KB (203 words) - 09:19, 5 February 2024
- ...e problem consists of determining the optimal packing of a given number of spheres inside the cube. | title = Dense packings of equal spheres in a cube ...3 KB (458 words) - 05:49, 20 May 2024
- ...on|Topological degree is the only homotopy invariant of continuous maps to spheres}} ...967 bytes (135 words) - 18:44, 10 October 2020
- ...gest empty sphere in the [[Close-packing of equal spheres|close-packing of spheres]]. See also ''[[Interstitial defect]]''.]] ...2 KB (219 words) - 01:19, 19 April 2023
- ...ection of spheres with point dipoles embedded at the centre of each. These spheres ...d-Jones and dipolar interactions. In the absence of the point dipoles, the spheres face no rotational ...3 KB (396 words) - 08:22, 30 June 2024
- {{short description|On the loop space of a wedge of spheres}} ...nce|homotopy-equivalent]] to a [[product space|product]] of loop spaces of spheres. ...3 KB (423 words) - 08:42, 27 December 2024
- ...[[integral|integrating]] over [[sphere]]s, one integrates over generalized spheres: for a homogeneous space ''X'' = ''G''/''H'', a '''generalized sp ...|compact]] [[subgroup]]. Generalized spheres are then actual [[geodesic]] spheres and the spherical averaging operator is defined as ...3 KB (517 words) - 15:22, 1 January 2024
- ...ince Gauss, Laves phases are the result of his investigations into packing spheres of two sizes. Laves phases fall into three [[Strukturbericht designation|St ...V. | doi = 10.1080/01418618008239380 | title = Close-packed structures of spheres of two different sizes II. The packing densities of likely arrangements | j ...4 KB (533 words) - 20:15, 3 April 2024
- ...em exists in three dimensions for the intersection of two [[sphere]]s. The spheres <math>k_1</math> and <math>k_2</math> intersect in the circle <math>k_s</ma ...journal)|Mathesis]]. Eight years later he published ''On Two Intersecting Spheres'' in the [[American Mathematical Monthly]], which contained the 3-dimension ...3 KB (537 words) - 17:23, 15 September 2024
- ...year=1935}} in the case when ''<math>X</math>'' and ''<math>Y</math>'' are spheres. {{harvtxt|Whitehead|1942}} used it to define the [[J-homomorphism]]. ...ion | last1=Whitehead | first1=George W. | title=On the homotopy groups of spheres and rotation groups | jstor=1968956 | mr=0007107 | year=1942 | journal=[[An ...2 KB (362 words) - 13:50, 12 January 2024
- ...cient and necessary condition]] for the [[Radius|radii]] of two [[N-sphere|spheres]] and the distance of their centers, so that a [[simplex]] exists, which is For two spheres (<math>2</math>-spheres) with respective radii <math>r</math> and <math>R</math>, fulfilling <math> ...6 KB (831 words) - 16:43, 4 January 2025
- ...ve the possible smooth structures on spheres, hence [[Exotic sphere|exotic spheres]]. They are named after the French mathematician [[Michel Kervaire]] and th ...ively doesn't have holes. This is possible with [[Homotopy sphere|homotopy spheres]], which are closed smooth manifolds with the same homotopy type as a spher ...7 KB (1,007 words) - 08:26, 15 February 2025
- ...a ''reducible'' cyclide. A reducible cyclide either splits into a union of spheres/planes or [[degeneracy (mathematics)|degenerates]] to a curve in [[R^3|<mat ...is generated as a canal surface (the envelope of a one-parameter family of spheres).<ref name="arxiv1"/> ...5 KB (688 words) - 12:45, 13 January 2025
- {{Short description|In-depth exploration of circles, spheres, and inversive geometry by Julian Coolidge}} ...degenerate spheres) with the inversions through them, and to coordinatize spheres by "pentacyclic coordinates".{{r|steinke}} ...6 KB (784 words) - 21:57, 2 April 2024
- ...icular, {{mvar|k}}-spheres centered at the origin are mapped to {{mvar|k}}-spheres centered at the origin. ...6 KB (893 words) - 05:44, 9 February 2024
- | known_for = [[Homotopy groups of spheres]] ...of the Adams spectral sequence and the 2-primary stable homotopy groups of spheres up to dimension 64 together with Michael Barratt, Martin Tangora, and Stanl ...6 KB (778 words) - 10:58, 7 April 2024
- ...ere bundle, is a [[fibration]] whose fibers are [[homotopy equivalent]] to spheres. For example, the fibration ...3 KB (461 words) - 17:47, 28 June 2022
- ...ption|Connects the homology of the symmetric groups with mapping spaces of spheres}} ...ion between the homology of the [[symmetric group]]s and mapping spaces of spheres. The theorem (named after Michael Barratt, Stewart Priddy, and [[Daniel Qui ...9 KB (1,422 words) - 08:04, 6 August 2023
- ===Exotic spheres=== ...5 KB (731 words) - 01:42, 11 December 2024