*Who is the founder of geometry on a sphere? you mean.

Bernhard Riemann http://en.wikipedia.org/wiki/Bernhard_Riemann 1) "Spherical geometry is the geometry of the two-dimensional surface of a sphere. It is an example of a non-Euclidean geometry. " Source and further information: http://en.wikipedia.org/wiki/Spherical_geometry "Bernhard Riemann, in a famous lecture in 1854, founded the field of Riemannian geometry, discussing in particular the ideas now called manifolds, Riemannian metric, and curvature. He constructed an infinite family of non-Euclidean geometries by giving a formula for a family of Riemannian metrics on the unit ball in Euclidean space. Sometimes he is unjustly credited with only discovering elliptic geometry; but in fact, this construction shows that his work was far-reaching, with his theorems holding for all geometries." Source and further information: http://en.wikipedia.org/wiki/Non-Euclidean_geometry 2) Another type of non-Euclidean geometry is hyperbolic geometry. "Around 1830, the Hungarian mathematician János Bolyai and the Russian mathematician Nikolai Ivanovich Lobachevsky separately published treatises on hyperbolic geometry. Consequently, hyperbolic geometry is called Bolyai-Lobachevskian geometry, as both mathematicians, independent of each other, are the basic authors of non-Euclidean geometry." Source and further information: http://en.wikipedia.org/wiki/Non-Euclidean_geometry