Spheres

A ball is a round object (usually spherical, but sometimes ovoid) with several uses. It is used in ball games, where the play of the game follows the state of the ball as it is hit, kicked or thrown by players. Balls can also be used for simpler activities, such as catch or juggling. Balls made from hard-wearing materials are used in engineering applications to provide very low friction bearings, known as ball bearings. Black-powder weapons use stone and metal balls as projectiles.

A sphere (from Ancient Greek , ) is a surface analogous to the circle, a curve. In solid geometry, a sphere is the set of points that are all at the same distance from a given point in three-dimensional space. That given point is the center of the sphere, and the distance is the sphere's radius. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians.

thumb|Topography globe featuring physical features of the Earth A globe is a spherical model of Earth, of some other celestial body, or of the celestial sphere. Globes serve purposes similar to maps, but, unlike maps, they do not distort the surface that they portray except to scale it down. A model globe of Earth is called a terrestrial globe. A model globe of the celestial sphere is called a celestial globe.

imaginary sphere of arbitrarily large radius, concentric with the observer

in mathematics, space bounded by a sphere

model of the extended complex plane plus a point at infinity

assertion that the Earth is (at least approximately) spherical

In geometry, a pseudosphere is a surface in \mathbb{R}^3. It is the most famous example of a pseudospherical surface. A pseudospherical surface is a surface piecewise smoothly immersed in \mathbb{R}^3 with constant negative Gaussian curvature. A "pseudospherical surface of radius " is a surface in \mathbb{R}^3 having curvature −1/R2 at each point. Its name comes from the analogy with the sphere of radius , which is a surface of curvature 1/R2. Examples include the tractroid, Dini's surfaces, breather surfaces, and the Kuen surface.

theorem which states that there is no nonvanishing continuous tangent vector field on even-dimensional n-spheres

thumb|2-sphere wireframe as an orthogonal projection right|thumb|Just as a stereographic projection can project a sphere's surface to a plane, it can also project a -sphere into -space. This image shows three coordinate directions projected to -space: parallels (red), meridians (blue), and hypermeridians (green). Due to the conformal property of the stereographic projection, the curves intersect each other orthogonally (in the yellow points) as in 4D. All of the curves are circles: the curves that intersect have an infinite radius (= straight line).

type of star chart where the map is arranged on a globe

mathematical theorem about sphere packing

sphere contained within a polyhedron, tangent to each of its faces

set of points in 3D space of distance 1 from a fixed central point

sphere that contains a polyhedron and touches each of the vertices thereof

dense arrangement of congruent spheres in an infinite, regular arrangement

mathematical concept

an arrangement of non-overlapping spheres within a containing space

thumb|A polyhedron and its midsphere. A viewer situated at a polyhedron vertex would see the red circle surrounding that vertex as the horizon on the sphere.|alt=An opaque white polyhedron with four triangular faces and four quadrilateral faces is crossed by a transparent blue sphere of approximately the same size, tangent to each edge of the polyhedron. The visible portions of the sphere, outside the polyhedron, form circular caps on each face of the polyhedron, of two sizes: smaller in the triangular faces, and larger in the quadrilateral faces. Red circles on the surface of the sphere, pass

thumb|Stereographic projection of the hypersphere's parallels (red), meridians (blue) and hypermeridians (green). Because this projection is conformal, the curves intersect each other orthogonally (in the yellow points) as in 4D. All curves are circles: the curves that intersect have infinite radius (= straight line). 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. thumb|Direct projection of 3-sphere into 3D space and covered with surface grid, showing structure as stack of 3D spher

small mineral objects, often spherical to disc-shaped, found in pyrophyllite deposits near Ottosdal, South Africa

energy conservation during diffraction by atoms

tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions

thumb|300px|Schematic representation of difference in grain shape. Two parameters are shown: sphericity (vertical) and Roundness (geology)|rounding (horizontal).

topological manifold whose homology coincides with that of a sphere, i.e. trivial except in the top and bottom degrees, where it has a single generator

smooth manifold that is homeomorphic but not diffeomorphic to a sphere

spherical projection system created by NOAA which presents high-resolution video on a suspended globe

concentric hollow spheres carved from a single solid block

sphere that contains a set of objects

how spheres of various dimensions can wrap around each other