Synonymer & Information om | Engelska ordet HYPERSPHERE

Exempel på hur man kan använda HYPERSPHERE i en mening

• In mathematics, an -sphere or hypersphere is an -dimensional generalization of the -dimensional circle and -dimensional sphere to any non-negative integer.
• In this picture, the whole 3D space maps the surface of the hypersphere, whereas in the next picture the 3D space contained the shadow of the bulk hypersphere.
• However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes circle packing in two dimensions, or hypersphere packing in higher dimensions) or to non-Euclidean spaces such as hyperbolic space.
• This behavior is matched by the set of unit quaternions: A general quaternion represents a point in a four-dimensional space, but constraining it to have unit magnitude yields a three-dimensional space equivalent to the surface of a hypersphere.
• Double factorials also arise in expressing the volume of a hyperball and surface area of a hypersphere, and they have many applications in enumerative combinatorics.
• In differential topology, the Hopf fibration (also known as the Hopf bundle or Hopf map) describes a 3-sphere (a hypersphere in four-dimensional space) in terms of circles and an ordinary sphere.
• After normalizing embeddings to the surface of a hypersphere, FaceNet achieves the best performance using 128 dimensions as opposed to 64, 256, or 512 dimensions in one ablation study.
• Hyperbolic motions are often taken from inversive geometry: these are mappings composed of reflections in a line or a circle (or in a hyperplane or a hypersphere for hyperbolic spaces of more than two dimensions).
• More generally, a gnomonic projection can be taken of any -dimensional hypersphere onto a hyperplane.
• A hypersphere in 5-space (also called a 4-sphere due to its surface being 4-dimensional) consists of the set of all points in 5-space at a fixed distance r from a central point P, that is rotationally symmetrical.
• These are just the rules for dualising four-dimensional 4-polytopes, except that the usual finite method of reciprocation about a concentric hypersphere can run into problems.

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