- Spherical geometry
**Spherical geometry**is thegeometry of the two-dimension al surface of asphere . It is an example of anon-Euclidean geometry . Two practical applications of the principles of spherical geometry arenavigation andastronomy .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 ageodesic . On the sphere the geodesics are thegreat circle s, so the other geometric concepts are defined like in plane geometry but with lines replaced by great circles. Thus, in spherical geometryangle s are defined between great circles, resulting in aspherical trigonometry that differs from ordinarytrigonometry in many respects (for example, the sum of the interior angles of a triangle exceeds 180 degrees).Spherical geometry is the simplest model of

elliptic geometry , in which a line has no parallels through a given point. Contrast this withhyperbolic geometry , in which a line has two parallels, and an infinite number of ultra-parallels, through a given point.An important related geometry related to that modeled by the sphere is called the

real projective plane ; it is obtained by identifying antipodes (pairs of opposite points) on the sphere. Locally, the projective plane has all the properties of spherical geometry, but it has different global properties. In particular, it is non-orientable.**ee also***Spherical distance

*Spherical polyhedron

*Spherical trigonometry

*SIGI **External links*** [

*http://www.math.uncc.edu/~droyster/math3181/notes/hyprgeom/node5.html Spherical Geometry*] UNCC

* [*http://math.rice.edu/~pcmi/sphere/ The Geometry of the Sphere*]Rice University

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