-dimensional sphere to any non-negative integer n {\displaystyle n} . The n {\displaystyle n} -sphere is the setting for n {\displaystyle n} -dimensional...
37 KB (7,130 words) - 10:34, 22 August 2024
"the" n-sphere. The ordinary sphere is a 2-sphere, because it is a 2-dimensional surface which is embedded in 3-dimensional space. In topology, the n-sphere...
41 KB (5,331 words) - 01:06, 31 August 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 (4,027 words) - 22:10, 31 August 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 (1,529 words) - 01:47, 27 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....
77 KB (6,175 words) - 16:50, 9 September 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) - 13:26, 28 May 2024
The Sphere (officially Große Kugelkaryatide N.Y., also known as Sphere at Plaza Fountain, WTC Sphere or Koenig Sphere) is a monumental cast bronze sculpture...
24 KB (2,230 words) - 20:56, 9 September 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 (7,972 words) - 00:30, 24 August 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...
1 KB (172 words) - 18:09, 27 May 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...
29 KB (5,448 words) - 14:09, 8 September 2024