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Spherical geometry

Spherical Geometry

The study of the figure on the two dimensional surface of the sphere is called as Spherical Geometry. Its principle is practically applied for navigation and astronomy. It is the best example of geometry which is not euclidean.

In spherical geometry, the points are points that lies on the surface of the sphere. The shortest paths between the points is called as Geodesics. Lines in the spherical geometry is subtle and more curved. Thus, instead of lines geodesics is used while referring the spherical geometry.

A great circle on the sphere which divides the sphere into two hemisphere. The shortest distance between the two point of the sphere lies along the great circle. So, geodesics in spherical geometry are great circles.

The fundamental result of Euclidean geometry is always 180° for the sum of the angles of a triangle. Since there is no parallel lines in spherical triangle, the sum of the angles in any spherical sphere always exceeds 180°.

Real projective geometry can be best related to the spherical geometry, because it is obtained by identifying the antipodal points (pair of opposite points) on the sphere. It differs only in the global property because its non-orientable and one sided.

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