sphere
1. Mathsa. a three-dimensional closed surface such that every point on the surface is equidistant from a given point, the centre
b. the solid figure bounded by this surface or the space enclosed by it. Equation: (x--a)2 + (y--b)2 + (z--c)2 = r2, where r is the radius and (a, b, c) are the coordinates of the centre; surface area: 4πr2; volume: 4πr3/3
2. the night sky considered as a vaulted roof; firmament
3. any heavenly object such as a planet, natural satellite, or star
4. (in the Ptolemaic or Copernican systems of astronomy) one of a series of revolving hollow globes, arranged concentrically, on whose transparent surfaces the sun (or in the Copernican system the earth), the moon, the planets, and fixed stars were thought to be set, revolving around the earth (or in the Copernican system the sun)
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
sphere
[sfir] (mathematics)
The set of all points in a euclidean space which are a fixed common distance from some given point; in Euclidean three-dimensional space the Riemann sphere consists of all points (x,y,z) which satisfy the equation x 2 + y 2 + z 2=1.
The set of points in a metric space whose distance from a fixed point is constant.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.
Sphere
a closed surface all points of which are equally distant from a fixed point called the center of the sphere. A line segment joining the center and any of the points of a sphere is called the radius of the sphere. The term “radius” is also applied to the length of the segment. The area of a sphere is S = 4πR2, where R is the sphere’s radius.
The portion of space bounded by a sphere and containing its center is also called a sphere. The volume of such a portion of space is V = 4π/R3/3.
From the standpoint of analytic geometry, a sphere is a central quadric surface whose equation in rectangular coordinates has the form
(x – a)2 + (y – b)2 + (z – c)2 = R2
where a, b, and c are the coordinates of the center of the sphere.
Sphere
the geometric solid generated by revolving a circle about its diameter. A sphere is the locus of points in space at a distance not greater than a specified distance R from a fixed point. The fixed point is called the center of the sphere, and R is known as the sphere’s radius. The volume of a sphere is V = 4πR3/3. The surface of a sphere is also called a sphere; its area is S = 4πR2.
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.