sphere

Also known as 2-sphere, orb

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.

AI overview

A sphere is a perfectly round three-dimensional shape where every point on its surface sits at an equal distance from a central point, much like how a circle works in two dimensions. Spheres matter because they are a fundamental geometric form that appears throughout mathematics, nature, and everyday objects like planets and balls, making them essential to understanding spatial relationships and physical properties of the world around us.

AI-generated from the Wikipedia summary — may contain errors.

Key facts

Polyhedron<! Please add only parameters that make sense for a sphere. >.name: Sphere
Polyhedron<! Please add only parameters that make sense for a sphere. >.image: File:Sphere wireframe 10deg 6r.svg
Polyhedron<! Please add only parameters that make sense for a sphere. >.caption: A perspective projection of a sphere
Polyhedron<! Please add only parameters that make sense for a sphere. >.euler: 2
Polyhedron<! Please add only parameters that make sense for a sphere. >.symmetry: Orthogonal group|
Polyhedron<! Please add only parameters that make sense for a sphere. >.type: Smooth surfaceAlgebraic surface

via Wikipedia infobox

Wikidata facts

Image: Sphere Quadric.png

Show 3 more facts

Commons category: Spheres
Euler characteristic: 2
Commons gallery: Sphere

Sources (4)

via Wikidata · CC0

~30 min read

Article

32 sections

Contents

Basic terminology
Equations
Parametric
Properties
Enclosed volume{{anchor|Volume}}
Surface area{{anchor|Area}}
Other geometric properties
Pencil of spheres
Properties of the sphere
Treatment by area of mathematics
Spherical geometry
Differential geometry
Topology
Curves on a sphere {{anchor|Curves}}
Circles
Loxodrome
Clelia curves
Spherical conics
Intersection of a sphere with a more general surface
Generalizations
Ellipsoids
Dimensionality
Metric spaces
History
Gallery
Regions
See also
Notes and references
Notes
References
Further reading
External links

The sphere is a fundamental surface 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.