hypersphere's Usage Examples:

The zero-dimensional hypersphere is a pair of points.

The hypersphere in 1 dimension is a pair of points, sometimes called a 0-sphere as its.

dimensions (where the problem becomes circle packing in two dimensions, or hypersphere packing in higher dimensions) or to non-Euclidean spaces such as hyperbolic.

A hypersphere in 5-space (also called a 4-sphere due to its surface being 4-dimensional).

moving to better positions in the search-space, which are sampled from a hypersphere surrounding the current position.

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.

This hypersurface is also a smooth manifold, and is called a hypersphere or an (n – 1)-sphere.

geometry, the largest empty sphere problem is the problem of finding a hypersphere of largest radius in d-dimensional space whose interior does not overlap.

Public hypersphere is a new kind of public sphere that has come into existence globally through the use of modern information technology, digital media.

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.

( n − 1 ) {\displaystyle (n-1)} -dimensional hypersphere all lie on the same "half" of the hypersphere.

spherical code with parameters (n,N,t) is a set of N points on the unit hypersphere in n dimensions for which the dot product of unit vectors from the origin.

a hypersphere in four dimensional space (a 3-sphere).

is referred to as an oversphere, and a 4-sphere is referred to as a hypersphere.

The hypersphere in 2 dimensions is a circle, sometimes called a 1-sphere (S1) because.