spherical geometry

spherical geometry

English

Noun

spherical geometry (usually uncountable, plural spherical geometries)

1. (geometry, uncountable) The geometry of the 2-dimensional surface of a sphere;
   (countable) a given geometry of the surface of a sphere; a geometry of the surface of a given sphere, regarded as distinct from that of other spheres.

   The basic concepts of Euclidean geometry of the plane are the point and the (straight) line; in spherical geometry, the corresponding concepts are the point and the great circle.

   Due to the way the geometry of a sphere's surface differs from that of the plane, spherical geometry has some features of a non-Euclidean geometry and is sometimes described as being one. Historically, however, spherical geometry was not considered a fully fledged (non-Euclidean) geometry capable of resolving the question of whether the parallel postulate is a logical consequence of the rest of Euclid's axioms of plane geometry.

   • 1972, Morris Kline, Mathematical Thought from Ancient to Modern Times: Volume 1, Oxford University Press, 1990, paperback, page 119,

     Spherical trigonometry presupposes spherical geometry, for example the properties of great circles and spherical triangles, much of which was already known; it had been investigated as soon as astronomy became mathematical, during the time of the later Pythagoreans.

   • 1994, Miles Reid (translator), Viacheslav V. Nikulin, Igor R. Shafarevich, Geometries and Groups, Springer, page 194,

     We start with spherical geometries. The two geometries on spheres of radiuses R₁ and R₂ are obviously identical if R₁ = R₂; moreover, the converse also holds.

   • 2008, Sherif Ghali, Introduction to Geometric Computing, Springer, page 272,

     To collect the boundary of the point set in the tree we pass a bounding box (for Euclidean geometries) or the universal set (for spherical geometries) to the root of the tree.

   • 2020, Marshall A. Whittlesey, Spherical Geometry and Its Applications, Taylor & Francis (CRC Press), unnumbered page,

     It has been at least fifty years since spherical geometry and spherical trigonometry have been a regular part of the high school or undergraduate curriculum.

Related terms

• spherical trigonometry

Translations

branch of geometry

Catalan: geometria esfèrica f French: géométrie sphérique f Georgian: სფერული გეომეტრია (speruli geomeṭria) German: sphärische Geometrie f, Kugelgeometrie f, Geometrie auf der Kugel f Hungarian: gömbi geometria Italian: geometria sferica f Japanese: 球面幾何学 (ja) Portuguese: geometria esférica f Romanian: geometrie sferică Spanish: geometría esférica f Tagalog: timbuluging sukgisan

See also

• astrometry
• elliptic geometry
• great circle
• non-Euclidean geometry
• parallel postulate

Further reading

• Non-Euclidean geometry on Wikipedia.Wikipedia
  • Elliptic geometry on Wikipedia.Wikipedia
• Great circle on Wikipedia.Wikipedia
• Spherical trigonometry on Wikipedia.Wikipedia
• Spherical polyhedron on Wikipedia.Wikipedia
• Spherical astronomy on Wikipedia.Wikipedia
  • Celestial coordinate system on Wikipedia.Wikipedia
• Spherical geometry on Encyclopedia of Mathematics