- In mathematics, an n-sphere or
hypersphere is an n {\displaystyle n} -dimensional
generalization of the 1 {\displaystyle 1} -dimensional circle...
-
public sphere; it has a
whole new structure.
Mathematicians talk
about hyperspheres when they want to
describe a
sphere of
higher dimensionality,
where normal...
- a
hypersphere in four-dimensional
space (a 3-sphere). Just as in the
simpler example above, each
rotation represented as a
point on the
hypersphere is...
-
densest lattice ****ngs of
hyperspheres are
known up to 8 dimensions. Very
little is
known about irregular hypersphere ****ngs; it is
possible that...
- In mathematics, a
hypersphere or 3-sphere is a 4-dimensional
analogue of a sphere, and is the 3-dimensional n-sphere. In 4-dimensional
Euclidean space...
-
quadratic equation applies to
systems of
pairwise tangent spheres or
hyperspheres.
Geometrical problems involving tangent circles have been
pondered for...
- 0^{0}=1} .) The
support of the Von Mises–Fisher
distribution is the
hypersphere, or more specifically, the ( p − 1 ) {\displaystyle (p-1)} -sphere, denoted...
- {\displaystyle n} ≤ 4 {\displaystyle 4} .
There are four Hopf
fibrations of
hyperspheres: S 0 ↪ S 1 → S 1 , S 1 ↪ S 3 → S 2 , S 3 ↪ S 7 → S 4 , S 7 ↪ S 15 → S...
-
Platonic Solid Sphere Tetrahedron Four- / other-dimensional
Tesseract Hypersphere Geometers by name Aida
Aryabhata Ahmes Alhazen Apollonius Archimedes...
- For example, a
hypersphere would appear first as a point, then as a
growing sphere (until it
reaches the "hyperdiameter" of the
hypersphere), with the sphere...
