Sphere
A sphere (from Greek σφαῖρα — sphaira, "globe, ball") 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).
Description
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.
Distiction between sphere and 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)
- 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.
See also
- 3-sphere
- Affine sphere
- Alexander horned sphere
- Ball (mathematics)
- Banach–Tarski paradox
- Circle
- Circle of a sphere
- Cube
- Cuboid
- Curvature
- Curve
- Diameter
- Directional statistics
- Dome (mathematics)
- Dyson sphere
- Geometry
- Hoberman sphere
- Homology sphere
- Homotopy groups of spheres
- Homotopy sphere
- Hypersphere
- Lenart Sphere
- Metric space
- Napkin ring problem
- Pi
- Pseudosphere
- Riemann sphere
- Solid angle
- Sphere packing
- Spherical cap
- Spherical coordinates
- Spherical Earth
- Spherical helix, tangent indicatrix of a curve of constant precession
- Spherical sector
- Spherical segment
- Spherical shell
- Spherical wedge
- Spherical zone
- Translation of axes
- Zoll sphere
External links
- Sphere @ Wikipedia
