The first recorded study of spherical geometry was by Autolycus of Pitane, in the 4th century BC.
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Pilots and captains of ship use spherical geometry to navigate their working wheel to move it. They can measure their pathway and destiny by using Spherical Geometry.
There is a beautiful proof of Euler's Therom, using the area of the sphere and spherical geometry.
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It is the geometry of a sphere as well as of shapes on the surface of the sphere.
No, both spherical and hyperbolic geometries are noneuclidian.