n-sphere or hypersphere is an n-dimensional generalization of the 1-dimensional circle and 2-dimensional sphere to any non-negative integer n. The n-sphere... 38 KB (5,971 words) - 08:27, 4 May 2024 |
A sphere (from Greek σφαῖρα, sphaîra) is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. Formally, a sphere is the... 40 KB (5,274 words) - 14:34, 4 May 2024 |
Sphere (also called Sphere at the Venetian Resort) is a music and entertainment arena in Paradise, Nevada, United States, east of the Las Vegas Strip.... 67 KB (5,180 words) - 15:00, 3 May 2024 |
"surface"). Topologically, a 3-sphere is an example of a 3-manifold, and it is also an n-sphere. In coordinates, a 3-sphere with center (C0, C1, C2, C3)... 28 KB (3,996 words) - 01:30, 31 March 2024 |
generally, the unit n {\displaystyle n} -sphere is an n {\displaystyle n} -sphere of unit radius in ( n + 1 ) {\displaystyle (n+1)} -dimensional Euclidean... 12 KB (1,911 words) - 04:35, 4 May 2024 |
The n-dimensional unit sphere — called the n-sphere for brevity, and denoted as Sn — generalizes the familiar circle (S1) and the ordinary sphere (S2)... 82 KB (7,952 words) - 22:39, 25 April 2024 |
the region enclosed by a sphere or hypersphere. An n-ball is a ball in an n-dimensional Euclidean space. The volume of a n-ball is the Lebesgue measure... 28 KB (5,444 words) - 18:27, 31 March 2024 |
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical... 28 KB (3,328 words) - 17:59, 30 April 2024 |
homology sphere is an n-manifold X having the homology groups of an n-sphere, for some integer n ≥ 1 {\displaystyle n\geq 1} . That is, H 0 ( X , Z ) = H n (... 11 KB (1,555 words) - 01:17, 25 November 2023 |
intersection of a sphere and a plane passing through the sphere's center point. Any arc of a great circle is a geodesic of the sphere, so that great circles... 7 KB (972 words) - 05:55, 19 March 2024 |
Ball (mathematics) (redirect from Solid sphere) spaces in general. A ball in n dimensions is called a hyperball or n-ball and is bounded by a hypersphere or (n−1)-sphere. Thus, for example, a ball in... 12 KB (1,654 words) - 06:50, 31 March 2024 |
Manifold (section n-Sphere as a patchwork) normal bundle. The n-sphere Sn is a generalisation of the idea of a circle (1-sphere) and sphere (2-sphere) to higher dimensions. An n-sphere Sn can be constructed... 67 KB (9,476 words) - 21:20, 15 February 2024 |
exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n-sphere. That is, M is a sphere from... 28 KB (3,802 words) - 17:44, 10 April 2024 |
homotopy sphere is an n-manifold that is homotopy equivalent to the n-sphere. It thus has the same homotopy groups and the same homology groups as the n-sphere... 2 KB (183 words) - 03:41, 14 April 2023 |
Spherical lune (section n-sphere lunes) tessellation of the sphere by lunes. A n-gonal regular hosohedron, {2,n} has n equal lunes of π/n radians. An n-hosohedron has dihedral symmetry Dnh, [n,2], (*22n)... 5 KB (576 words) - 08:08, 24 January 2024 |
sphere-like region or shell. Sphere may also refer to: Armillary sphere, a physical model of the celestial sphere Celestial sphere, the astronomical description... 5 KB (607 words) - 01:15, 11 February 2024 |
Then the statement is Every homotopy sphere (a closed n-manifold which is homotopy equivalent to the n-sphere) in the chosen category (i.e. topological... 10 KB (1,292 words) - 18:39, 7 April 2024 |
De Rham cohomology (section The n-sphere) objects: For the n-sphere, S n {\displaystyle S^{n}} , and also when taken together with a product of open intervals, we have the following. Let n > 0, m ≥ 0... 19 KB (2,921 words) - 03:10, 13 August 2023 |
In mathematics, two points of a sphere (or n-sphere, including a circle) are called antipodal or diametrically opposite if they are the endpoints of a... 4 KB (509 words) - 18:35, 31 March 2024 |
function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point. Here, two points on a sphere are called antipodal... 14 KB (2,326 words) - 15:54, 26 April 2024 |
topology, it is often denoted as S1 because it is a one-dimensional unit n-sphere. If (x, y) is a point on the unit circle's circumference, then |x| and... 8 KB (1,009 words) - 03:19, 19 April 2024 |
Inversive geometry (redirect from Sphere inversion) orthogonal to the unit sphere. Hence we are led to consider the (n − 1)-spheres with equation x 1 2 + ⋯ + x n 2 + 2 a 1 x 1 + ⋯ + 2 a n x n + 1 = 0 , {\displaystyle... 30 KB (4,378 words) - 02:03, 11 April 2024 |
Spherical measure (redirect from Sphere measure) "natural" Borel measure on the n-sphere Sn. Spherical measure is often normalized so that it is a probability measure on the sphere, i.e. so that σn(Sn) = 1... 5 KB (670 words) - 05:38, 23 December 2021 |
Real projective space (redirect from RP^n) Thus RPn can also be formed by identifying antipodal points of the unit n-sphere, Sn, in Rn+1. One can further restrict to the upper hemisphere of Sn and... 11 KB (1,634 words) - 21:23, 14 July 2023 |
attribute of the Lightweight Directory Access Protocol Symmetric group or Sn n-sphere or Sn sn (elliptic function), one of Jacobi's elliptic functions SN, METAR... 2 KB (340 words) - 00:56, 8 December 2022 |
armillary sphere (variations are known as spherical astrolabe, armilla, or armil) is a model of objects in the sky (on the celestial sphere), consisting... 33 KB (4,357 words) - 04:05, 4 May 2024 |
proof of the sphere theorem did not conclude that M was necessarily diffeomorphic to the n-sphere. This complication is because spheres in higher dimensions... 5 KB (591 words) - 01:37, 20 February 2024 |