# spherical geometry

## English

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### Noun

spherical geometry (usually uncountable, plural spherical geometries)

1. () 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, Viacheslav V. Nikulin; Igor R. Shafarevich, Miles Reid, transl., 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.