A sphere (from Ancient Greek σφαῖρα (sphaîra) 'globe, ball')[1] is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. Formally, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space.[2] That given point is the centre of the sphere, and r is the sphere's radius. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians.

TypeSmooth surface
Algebraic surface
Euler char.2
Symmetry groupO(3)
Surface area4πr2

The sphere is a fundamental object in many fields of mathematics. Spheres and nearly-spherical shapes also appear in nature and industry. Bubbles such as soap bubbles take a spherical shape in equilibrium. The Earth is 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 mirrors and lenses are based on spheres. Spheres roll smoothly in any direction, so most balls used in sports and toys are spherical, as are ball bearings.

Geometrically, a sphere can be formed by rotating a circle one half revolution around an axis that intersects the center of the circle, or by rotating a semicircle one full revolution around the axis that is coincident (or concurrent) with the straight edge of the semicircle.

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