Sphere vs. Hemisphere - What's the difference?

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). Like a circle, which geometrically is an object in two-dimensional space, 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. These are also referred to as the radius and center of the sphere, respectively. 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 (sphere) 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) and the ball (a three-dimensional shape that includes the sphere as well as everything inside the sphere). This distinction has not always been maintained and there are mathematical references, especially older ones, that talk about a sphere as a solid. This is analogous to the situation in the plane, where the terms "circle" and "disk" are confounded.

Sphere vs. Hemisphere

Hemisphere

Sphere

1. Alternative forms

  • sphære (archaic)
  • sphear (archaic)

2. Etymology

From Old French sphere, from Late Latin sphēra, earlier Latin sphaera (ball, globe, celestial sphere), from Ancient Greek σφαῖρα (sphaîra, ball, globe), of unknown origin. Compare Persian سپهر‎ (sepehr, sky)

3. Pronunciation

  • (UK) IPA(key): /sfɪə/
  • (US) enPR: sfîr, IPA(key): /sfɪɹ/
  • Rhymes: -ɪə(r)

4. Noun

sphere (plural spheres)

  1. (mathematics) A regular three-dimensional object in which every cross-section is a circle; the figure described by the revolution of a circle about its diameter [from 14th c.].
  2. A spherical physical object; a globe or ball. [from 14th c.]
    • Milton
      Of celestial bodies, first the sun, / A mighty sphere, he framed.
    • 2011, Piers Sellers, The Guardian, 6 July:
      So your orientation changes a little bit but it sinks in that the world is a sphere, and you're going around it, sometimes under it, sideways, or over it.
  3. (astronomy, now rare) The apparent outer limit of space; the edge of the heavens, imagined as a hollow globe within which celestial bodies appear to be embedded. [from 14th c.]
    • 1635, John Donne, "His parting form her":
      Though cold and darkness longer hang somewhere, / Yet Phoebus equally lights all the Sphere.
  4. (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). [from 14th c.]
    • , vol.1, p.153:
      It is more simplicitie to teach our children [] [t]he knowledge of the starres, and the motion of the eighth spheare, before their owne.
    • 1646, Thomas Browne, Pseudodoxia Epidemica, I.6:
      They understood not the motion of the eighth sphear from West to East, and so conceived the longitude of the Stars invariable.
  5. (mythology) An area of activity for a planet; or by extension, an area of influence for a god, hero etc. [from 14th c.]
  6. (figuratively) The region in which something or someone is active; one's province, domain. [from 17th c.]
    • 1946, Bertrand Russell, History of Western Philosophy, I.20:
      They thought – originally on grounds derived from religion – that each thing or person had its or his proper sphere, to overstep which is ‘unjust’.
  7. (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 [from 20th c.].
  8. (logic) The extension of a general conception, or the totality of the individuals or species to which it may be applied.

4.1. Synonyms

  • (object): ball, globe, orb
  • (region of activity): area, domain, field, orbit, sector
  • (in geometry): 3-sphere (geometry), 2-sphere (topology)
  • (astronomy: apparent surface of the heavens): See celestial sphere
  • (astronomy: anything visible on the apparent surface of the heavens): See celestial body

4.2. Derived terms

  • blogosphere
  • sphere of influence
  • sphere of interest
  • atmosphere
  • hemisphere
  • ionosphere
  • planisphere
  • spherical
  • spheroid
  • stratosphere
  • troposphere

5. Verb

sphere (third-person singular simple present spheres, present participle sphering, simple past and past participle sphered)

  1. (transitive) To place in a sphere, or among the spheres; to ensphere.
    • Shakespeare
      The glorious planet Sol / In noble eminence enthroned and sphered / Amidst the other.
  2. (transitive) To make round or spherical; to perfect.
    (Can we find and add a quotation of Tennyson to this entry?)

6. See also

  • ball (in topology)
  • Mathworld article on the sphere
  • PlanetMath article on the sphere

7. Anagrams

  • Hesper, herpes, pesher, pheers

Hemisphere

1. Alternative forms

  • hemisphære (archaic)

2. Etymology

From Latin hemisphaerium, from Ancient Greek ἡμισφαίριον (hēmisphaírion), from ἡμι- (hēmi-, half) + σφαῖρα (sphaîra, sphere); hemi- +‎ sphere

3. Pronunciation

  • (Received Pronunciation) IPA(key): /ˈhɛmɪsfɪə/
  • (US) enPR: hĕ'mĭsfîr, IPA(key): /ˈhɛmɪsfɪəɹ/

4. Noun

hemisphere (plural hemispheres)

  1. (astronomy, astrology) Half of the celestial sphere, as divided by either the ecliptic or the celestial equator [from 14th c.].
  2. (figuratively) A realm or domain of activity [1503].
  3. (geography) Half of the Earth, such as the Northern Hemisphere, Southern Hemisphere, Western Hemisphere or Eastern Hemisphere, Land Hemisphere, Water Hemisphere etc. [1550s].
  4. (geometry) Any half-sphere, formed by a plane intersecting the center of a sphere. [1580s].
  5. (cartography) A map or projection of a celestial or terrestrial hemisphere [1706].
  6. (anatomy) Either of the two halves of the cerebrum. [1804].

4.1. Synonyms

  • (astronomy: half of the celestial sphere): celestial hemisphere
  • (geography: half of the terrestrial sphere): terrestrial hemisphere
  • (figuratively: a domain of thought or action): sphere
  • (geometry: half of a sphere): half-sphere, half sphere
  • (anatomy: either of the two lobes of the cerebellum): cerebral hemisphere
  • (cartography: a map showing a projection of a hemisphere): planisphere
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