## ::Sphere

### ::concepts

Sphere::surface    Points::radius    Volume::''r''    Circle::geometry    Space::plane    Point::center

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A two-dimensional perspective projection of a sphere
r – radius of the sphere

A sphere (from Greek σφαῖρα — sphaira, "globe, ball"<ref>σφαῖρα, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus</ref>) is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball, (viz., analogous to a circular object in two dimensions).<ref> Beddoe, Jennifer - Sphere: Definition & Formulas - Study.com. Retrieved 15 July 2015.</ref> Like a circle, which geometrically is a two-dimensional object, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point, but in three-dimensional space. This distance r is the radius of the ball, and the given point is the center of the mathematical ball. The longest straight line through the ball, connecting two points of the sphere, passes through the center and its length is thus twice the radius; it is a diameter of the ball.

While outside mathematics the terms "sphere" and "ball" are sometimes used interchangeably, in mathematics a distinction is made between the sphere (a two-dimensional closed surface embedded in three-dimensional Euclidean space) and the ball (a three-dimensional shape that includes the sphere as well as everything inside the sphere). The ball and the sphere share the same radius, diameter, and center.

Sphere sections
Intro  [[Sphere?section=Surface_area{{safesubst:#invoke:anchor|main}}|Surface area{{safesubst:#invoke:anchor|main}}]]  [[Sphere?section=_Enclosed_volume{{safesubst:#invoke:anchor|main}}_| Enclosed volume{{safesubst:#invoke:anchor|main}} ]]  Equations in three-dimensional space  Terminology  Hemisphere  Generalization to other dimensions  Generalization to metric spaces  Topology  Spherical geometry  Eleven properties of the sphere  Cubes in relation to spheres  See also  References  External links

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