See also
- 3-sphere In mathematics, a 3-sphere is a higher-dimensional analogue of a sphere. It consists of the set of points equidistant from a fixed central point in 4-dimensional Euclidean space. Just as an ordinary sphere is a two dimensional surface that forms the boundary of a ball in three dimensions, a 3-sphere is an object with three dimensions that forms
- Alexander horned sphere The Alexander horned sphere is one of the most famous pathological examples in mathematics discovered in 1924 by J. W. Alexander. It is the particular embedding of a sphere in 3-dimensional Euclidean space obtained by the following construction, starting with a standard torus:
- Ball (mathematics) In mathematics, a ball is the inside of a sphere; both concepts apply not only in the three-dimensional space but also for lower and higher dimensions, and for metric spaces in general
- Banach–Tarski paradox
- Cube inscribed in a sphere
- Curvature
- Directional statistics Directional statistics is the subdiscipline of statistics that deals with directions , axes (lines through the origin in Rn) or rotations in Rn. More generally, directional statistics deals with observations on compact Riemannian manifolds
- Dome (mathematics) In mathematics, a dome is a closed geometrical surface which can be obtained by sectioning off a portion of a sphere with an intersecting plane. It consists of two parts: a flat disk, which is joined to (2) a convex surface whose curvature is uniform and which has a circular boundary: this boundary joins with the rim of the disk. The disk can be
- Dyson sphere A Dyson sphere is a hypothetical megastructure originally described by Freeman Dyson. Such a "sphere" would be a system of orbiting solar power satellites meant to completely encompass a star and capture most or all of its energy output. Dyson speculated that such structures would be the logical consequence of the long-term survival and
- Hoberman sphere A Hoberman sphere is a structure that resembles a geodesic dome, but is capable of folding down to a fraction of its normal size by the scissor-like action of its joints. Colorful plastic versions have become popular as a child's toy: several toy sizes exist, with the original design capable of expanding from 15 cm in diameter to 76 cm (30 inches)
- Homology sphere In algebraic topology, a homology sphere is an n-manifold X having the homology groups of an n-sphere, for some integer n ≥ 1. That is,
- Homotopy groups of spheres In the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other. They are examples of topological invariants, which reflect, in algebraic terms, the structure of spheres viewed as topological spaces, forgetting about their precise geometry. Unlike homology groups,
- Homotopy sphere In algebraic topology, a branch of mathematics, a homotopy sphere is an n-manifold homotopy equivalent to the n-sphere. It thus has the same homotopy groups and the same homology groups, as the n-sphere. So every homotopy sphere is an homology sphere
- Hypersphere In mathematics, an n-sphere is a generalization of the surface of an ordinary sphere to arbitrary dimension. For any natural number n, an n-sphere of radius r is defined as the set of points in -dimensional Euclidean space which are at distance r from a central point, where the radius r may be any positive real number. It is an n-dimensional
- Metric space In mathematics, a metric space is a set where a notion of distance between elements of the set is defined
- Napkin ring problem In geometry, it is somewhat surprising that the volume of a band of specified height around a sphere does not depend on the sphere's radius
- Pseudosphere In geometry, a pseudosphere of radius R is a surface of curvature −1/R2 , by analogy with the sphere of radius R, which is a surface of curvature 1/R2. The term was introduced by Eugenio Beltrami in his 1868 paper on models of hyperbolic geometry
- Riemann sphere On a purely algebraic level, the complex numbers with an extra infinity element constitute a number system known as the extended complex numbers. Arithmetic with infinity does not obey all of the usual rules of algebra, and so the extended complex numbers do not form a field. However, the Riemann sphere is geometrically and analytically well-
- Smale's paradox In differential topology, Smale's paradox states that it is possible to turn a sphere inside out in 3-space with possible self-intersections but without creating any crease, a process often called sphere eversion . This is surprising, and is hence deemed a veridical paradox. More precisely, let
- Solid angle The solid angle, Ω, is the angle in three-dimensional space that an object subtends at a point. It is a measure of how big that object appears to an observer looking from that point. For instance, a small object nearby could subtend the same solid angle as a large object far away. The solid angle is equal to the area of the segment of unit sphere
- Sphere packing In mathematics, sphere packing problems concern arrangements of non-overlapping identical spheres which fill a space. Usually the space involved is three-dimensional Euclidean space. However, sphere packing problems can be generalised to two dimensional space , to n-dimensional space (where the "spheres" are hyperspheres) and to non-
- Spherical cap In geometry, a spherical cap is a portion of a sphere cut off by a plane. If the plane passes through the center of the sphere, so that the height of the cap is equal to the radius of the sphere, the spherical cap is called a hemisphere
- Spherical coordinates In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance from a fixed origin, the elevation angle of that point from a fixed plane, and the azimuth angle of its orthogonal projection on that plane, from a fixed direction on the
- Spherical Earth The concept of a spherical Earth dates back to around the 6th century BCE in ancient Greek philosophy. It remained a matter of philosophical speculation until the 3rd century BCE when Hellenistic astronomy established the spherical shape of the earth as a physical given
- Zoll sphere A Zoll surface, named after Otto Zoll, , is a surface homeomorphic to the 2-sphere, with a Riemannian metric all of whose geodesics are closed and of equal length
<<Table of Contents A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point. This distance r is known as the radius of the sphere. The | Next>>
