- In mathematics, an n-sphere or
hypersphere is an n-dimensional
generalization of the 1-dimensional
circle and 2-dimensional
sphere to any non-negative...
- 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...
-
public sphere; it has a
whole new structure.
Mathematicians talk
about hyperspheres when they want to
describe a
sphere of
higher dimensionality,
where normal...
- the
hyperspheres that
share a
tangent hyperplane at a
given point, as
their radii go
towards infinity. In
Euclidean geometry, such a "
hypersphere of infinite...
-
quadratic equation applies to
systems of
pairwise tangent spheres or
hyperspheres.
Geometrical problems involving tangent circles have been
pondered for...
-
densest lattice ****ngs of
hyperspheres are
known up to 8 dimensions. Very
little is
known about irregular hypersphere ****ngs; it is
possible that...
- {\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...
- (2013). "Precise
algorithm to
generate random sequential addition of hard
hyperspheres at saturation". Phys. Rev. E. 88 (5): 053312. arXiv:1402.4883. Bibcode:2013PhRvE...
- In mathematics, a 3-sphere,
glome or
hypersphere is a higher-dimensional
analogue of a sphere. In 4-dimensional
Euclidean space, it is the set of points...
- 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...
