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( Sphere)
A sphere (from Greek sfa??a - sphaira, "globe, ball,"[1]) is a symmetrical geometrical object. In non-mathematical usage, the term is used to refer either to a round ball or to its two-dimensional surface. In mathematics, a sphere is the set of all points in three-dimensional space (R3) which are at distance r from a fixed point of that space, where r is a positive real number called the radius of the sphere. Thus, in three dimensions, a mathematical sphere is considered to be a two-dimensional spherical surface embedded in three-dimensional space, rather than the volume contained within it (which mathematicians would instead describe as a ball). The fixed point is called the center, and is not part of the sphere itself. The special case of r = 1 is called a unit sphere. This article deals with the mathematical concept of a sphere. In physics, a sphere is an object (usually idealized for the sake of simplicity) capable of colliding or stacking with other objects which occupy space. In analytic geometry, a sphere with center (x0, y0, z0) and radius r is the locus of all points (x, y, z) such that The points on the sphere with radius r can be parametrized via
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