Editing Sphere (section)

{{Short description|Set of points equidistant from a center}}
{{About|the concept in three-dimensional geometry}}
{{Distinguish|Ball (mathematics)}}
{{pp-move-indef}}
{{Use dmy dates|date=June 2021}}
{{Infobox polyhedron<!--Please add only parameters that make sense for a sphere.-->
| name         = Sphere
| image        = File:Sphere wireframe 10deg 6r.svg
| caption      = A [[3D projection#Perspective projection|perspective projection]] of a sphere
| euler        = 2
| symmetry     = [[Orthogonal group|{{math|O(3)}}]]
| surface_area = {{math|4πr<sup>2</sup>}}
| volume       = {{math|{{sfrac|4|3}}πr<sup>3</sup>}}
| type         = [[Smooth surface]]{{br}}[[Algebraic surface]]
}}

A '''sphere''' (from [[Ancient Greek|Greek]] {{wikt-lang|grc|σφαῖρα}}, {{grc-transl|σφαῖρα}})<ref>[https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Dsfai%3Dra^ σφαῖρα], Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus.</ref> is a [[surface (mathematics)|surface]] analogous to the [[circle]], a [[curve]]. In [[solid geometry]], a sphere is the [[Locus (mathematics)|set of points]] that are all at the same distance {{math|''r''}} from a given point in [[three-dimensional space]].<ref name=Albert54>{{harvnb|Albert|2016|loc=p. 54}}.</ref> That given point is the [[center (geometry)|''center'']] of the sphere, and the distance {{math|''r''}} is the sphere's ''[[radius]]''. The earliest known mentions of spheres appear in the work of the [[Greek mathematics|ancient Greek mathematicians]].

The sphere is a fundamental surface in many fields of [[mathematics]]. Spheres and nearly-spherical shapes also appear in nature and industry. [[Bubble (physics)|Bubble]]s such as [[soap bubble]]s take a spherical shape in equilibrium. The Earth is [[spherical Earth|often approximated as a sphere]] in [[geography]], and the [[celestial sphere]] is an important concept in [[astronomy]]. Manufactured items including [[pressure vessels]] and most [[curved mirror]]s and [[lens]]es are based on spheres. Spheres [[rolling|roll]] smoothly in any direction, so most [[ball]]s used in sports and toys are spherical, as are [[ball bearings]].