# 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, 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.