The study of figures on the surface of a sphere (such as the spherical triangle and spherical polygon), as opposed to the type of geometry studied in plane geometry or solid geometry. In spherical geometry, straight lines are great circles, so any two lines meet in two points. There are also no parallel lines. The angle between two lines in spherical geometry is the angle between the planes of the corresponding great circles, and a spherical triangle is defined by its three angles. There is no concept of similar triangles in spherical geometry.
See alsoGreat Circle, Hyperbolic Geometry, Plane Geometry, Solid Geometry, Spherical Triangle, Spherical Trigonometry, Thurston's Geometrization Conjecture
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ReferencesHarris, J. W. and Stocker, H. "Spherical Geometry." §4.9 in Handbook of Mathematics and Computational Science. New York: Springer-Verlag, pp. 108-113, 1998.Henderson, D. W. Experiencing Geometry: On Plane and Sphere. Englewood Cliffs, NJ: Prentice-Hall, 1995.Hopf, H. "Selected Chapters of Geometry." ETH Zürich lecture, pp. 1-2, 1940. http://www.math.cornell.edu/~hatcher/Other/hopf-samelson.pdf.Zwillinger, D. (Ed.). "Spherical Geometry and Trigonometry." §6.4 in CRC Standard Mathematical Tables and Formulae. Boca Raton, FL: CRC Press, pp. 468-471, 1995.
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Weisstein, Eric W. "Spherical Geometry." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SphericalGeometry.html