Dictionary

spherical geometry en · NOUN

Meanings

1. (uncountable, usually) The geometry of the 2-dimensional surface of a sphere;
   • 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.
   • 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. 1994, Viacheslav V. Nikulin, Igor R. Shafarevich, translated by Miles Reid, Geometries and Groups, Springer, page 194:
   • 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.
   • 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.
   • 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. 2008, Sherif Ghali, Introduction to Geometric Computing, Springer, page 272:
2. (countable, usually) 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. ▸ 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.

Forms

Relateds

great circle · astrometry · non-Euclidean geometry · parallel postulate · elliptic geometry · spherical trigonometry

Translations (17)

uk сферична геометрія (branch of geometry) · tl timbuluging sukgisan (branch of geometry) · de Kugelgeometrie (branch of geometry) · ca geometria esfèrica (branch of geometry) · pt geometria esférica (branch of geometry) · fr géométrie sphérique (branch of geometry) · ru сферическая геометрия (branch of geometry) · it geometria sferica (branch of geometry) · ka სფერული გეომეტრია (branch of geometry) · de Geometrie auf der Kugel (branch of geometry) · es geometría esférica (branch of geometry) · pl geometria sferyczna (branch of geometry) · de sphärische Geometrie (branch of geometry) · hy ոլորտային երկրաչափություն (branch of geometry) · ro geometrie sferică (branch of geometry) · hu gömbi geometria (branch of geometry) · ja 球面幾何学 (branch of geometry)