sphere

1. (mathematics) A surface in three dimensions consisting of all points equidistant from a center. .Synonyms: 2-sphere

2. (astronomy, now rare) The celestial sphere: the edge of the heavens, imagined as a hollow globe within which celestial bodies appear to be embedded.Examples: "Though cold and darkness longer hang somewhere, / Yet Phoebus equally lights all the Sphere."; "Resistless rolls the illimitable sphere, / And one great circle forms the unmeasured year."archaic

3. (historical, astronomy, mythology) Any of the concentric hollow transparent globes formerly believed to rotate around the Earth, and which carried the heavenly bodies; there were originally believed to be eight, and later nine and ten; friction between them was thought to cause a harmonious sound (the music of the spheres).Examples: "ſooner ſhall the Sun fall from his Spheare, Than Tamburlaine be ſlaine or ouercome."; "It is more simplicitie to teach our children[…][t]he knowledge of the starres, and the motion of the eighth spheare, before their owne."; "They understood not the motion of the eighth sphear from West to East, and so conceived the longitude of the Stars invariable."historical

4. (mythology) An area of activity for a planet; or by extension, an area of influence for a god, hero etc.

5. (figuratively) The region in which something or someone is active; one's province, domain.Examples: "sphere of influence"; "...while his sweet and gentle niece would be a charming companion for Francesca; and he thought, with a glow of affection long unfelt, that Lucy Aylmer must inevitably make a friend whose future kindness might add much to her happiness. Both were at present placed out of their sphere: but the one would in all probability have it greatly in her power to cherish and aid the other."; "They thought – originally on grounds derived from religion – that each thing or person had its or his proper sphere, to overstep which is ‘unjust’."Synonyms: area, field, orbit, sectorfiguratively

6. (geometry) The set of all points in three-dimensional Euclidean space (or n-dimensional space, in topology) that are a fixed distance from a fixed point .