3-sphere - Wikipedia
Direct projection of 3-sphere into 3D space and covered with surface grid, showing structure as stack of 3D spheres (2-spheres) 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, it is the set of points equidistant from a fixed central point.
3-Dimensional Space | The spherical space $S^3$
The space $S^3$ is the 3-dimensional analogue of the usual sphere in 2 dimensions. It is an isotropic space (all the directions play the same role). Among the eight Thurston geometries, it is the only compact one.
Henri Poincar¿, His Conjecture, Copacabana and Higher Dimensions
2004年6月9日 · For 100 years mathematicians have been trying to prove a conjecture that was first proposed by Henri Poincar¿ relating to an object known as the three-dimensional sphere, or 3-sphere. The...
Sphere - Wikipedia
A sphere (from Greek σφαῖρα, sphaîra) [1] is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. Formally, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. [2] That given point is the center of the sphere, and r is the sphere's radius.
The 3-sphere: Extrinsic and Intrinsic Forms - ThatsMaths
2022年9月22日 · The 3-sphere is a compact, connected, 3-dimensional manifold without boundary. It is also simply connected: any loop on the 3-sphere can be continuously shrunk to a point without leaving the 3-sphere.
Sphere - Art of Problem Solving
Spheres are the natural 3-dimensional analog of circles. The volume of a sphere is , where r is the radius of the sphere. The surface area of a sphere is , where r is the radius. In a circle, a sector of measure covers the circumference and area of the entire …
Three Dimensional Figures - Andrews University
A sphere may be thought of as the three-dimensional analogue of a circle. Twice a radius is a diameter. A Hypersphere or 4-ball is a four dimensional analog of a sphere. (Analogue is purposely spelt differently, but also correctly here.) A ball (circle, sphere, hypersphere) in n dimensions is termed an n-ball.
Great Sphere -- from Wolfram MathWorld
4 天之前 · The great sphere on the surface of a hypersphere is the three-dimensional analog of the great circle on the surface of a sphere. Let 2h be the number of reflecting spheres, and let great spheres divide a hypersphere into g four-dimensional tetrahedra.
For this project, we developed real-time 3D graphics programs for visualization of point-cloud data sets in the 3-dimensional sphere. They target both virtual reality platforms (such as Google Cardboard and Oculus Rift) and desktop computers.
try to understand a 3-sphere. From the latest results of the theory of relativity it is probable that our three-dimensional space is also approximately spherical, that is, that the laws of disposition of rigid bodies in it are not given by Euclidean geom-etry, but approximately by spherical geometry, if only we consider parts