Spherical geometry is the
geometry of the two-
dimensional surface of a
sphere. It is an example of a
non-Euclidean geometry. Two practical applications of the principles of spherical geometry are
navigation and
astronomy.In
plane geometry the basic concepts are
points and
line. On the sphere, points are defined in the usual sense. The equivalents of lines are not defined in the usual sense of "straight line" but in the sense of "the shortest paths between points" which is called a
geodesic. On the sphere the geodesics are the
great circles, so the other geometric concepts are defined like in plane geometry but with lines replaced by great circles. Thus, in spherical geometry
angles are defined between great circles, resulting in a
spherical trigonometry that differs from ordinary
trigonometry in many respects (for example, the sum of the interior angles of a triangle exceeds 180 degrees).
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