sphere

n. round three-dimensional geometric figure whose surface is at all points equidistant from the center; ball, globe, orb; heavens, sky; celestial body, planet; domain, realm, area

A sphere is a symmetrical geometrical object. In non-mathematical usage, the term is used to refer either to a round ball or to its two-dimensional surface. In mathematics, a sphere is the set of all points in three-dimensional space (R3) which are at distance r from a fixed point of that space, where r is a positive real number called the radius of the sphere. Thus, in three dimensions, a mathematical sphere is considered to be a spherical surface, rather than the volume contained within it. The fixed point is called the center or centre, and is not part of the sphere itself. The special case of r = 1 is called a unit sphere.
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n. sphere, globe, area; field, range

(v. t.)
To place in a sphere, or among the spheres; to insphere.
  

(v. t.)
To form into roundness; to make spherical, or spheral; to perfect.
  

(n.)
The extension of a general conception, or the totality of the individuals or species to which it may be applied.
  

(n.)
The apparent surface of the heavens, which is assumed to be spherical and everywhere equally distant, in which the heavenly bodies appear to have their places, and on which the various astronomical circles, as of right ascension and declination, the equator, ecliptic, etc., are conceived to be drawn; an ideal geometrical sphere, with the astronomical and geographical circles in their proper positions on it.
  

(n.)
Rank; order of society; social positions.
  

(n.)
In ancient astronomy, one of the concentric and eccentric revolving spherical transparent shells in which the stars, sun, planets, and moon were supposed to be set, and by which they were carried, in such a manner as to produce their apparent motions.
  

(n.)
Hence, any globe or globular body, especially a celestial one, as the sun, a planet, or the earth.
  

(n.)
Circuit or range of action, knowledge, or influence; compass; province; employment; place of existence.
  

(n.)
An orbit, as of a star; a socket.
  

(n.)
A body or space contained under a single surface, which in every part is equally distant from a point within called its center.
  

Sphere Conventionally, the geometrical representative of the manifested one All, combining unity, comprehensiveness, simplicity, and symmetry; whereas the ever-unknown frontierless womb of boundless space is conventionally represented by the zero. All the sections of a sphere are circles; its surface is an infinite plane, having neither boundaries nor parts and therefore measurable perhaps solely by the rules of geometry. A balance of centrifugal and centripetal forces produces the sphere, as in a soap bubble. Its center and its surface represent opposite poles, between which radiate expansive and contractive energies. The earth is virtually a sphere. The heavens, the limits of our vision, form the surface of an ideal sphere, whose center is everywhere, and whose periphery is nowhere.
Also used in the sense of a region. Its meaning has analogies with the ideas connected with the circle.