We know the stereographic projection is a projective function from a plane to a sphere, so a sphere can be regarded as a plane by regarding the points of infinity as the same point. For this viewpoint, can a theorem of a plane be extended to one of a sphere? And what is the statement of this theorem? The purpose of this thesis is going to consider that how to project Steiner porism into a sphere by using the software “Cabri Geometry”.
Steiner porism is based on two discussions: inversion and a theorem of two disjoint circles. So in the first chapter, we will introduce the definition and properties of inverse function. In the second chapter, we will introduce the theorem of two disjoint circles which is a base for Steiner porism. And we will show origin Steiner porism on a plane in third chapter. In the forth chapter, we want to construct Steiner porism on sphere, and then we will show the properties of the Steiner chain in the last chapter.
All detail in this thesis is displayed on my side: http://www.oz.nthu.edu.tw/~g9621515, dynamically. You can view dynamical pages and constructing steps, even download my files there. But all rights there are reserved, just for pure non-commercial research.

[1]Bakel’man, I. IA. (Il’ia Iakovlevich), 1928- . Inversion/ I. Ya. Bakel’man; Translated and adapted from the Russian by Susan Williams and Joan W. Teller, Chicago:University of Chicago Press, 1974

[2]Coxeter, H. S. M. Introduction to Geometry, 2nd Ed. New York: Wiley, 1969

[3]Dorrie, Heinrich, 1873- . 100 great problems of elementary mathematics; their history and solution. / Translated by David Antin, New York: Dover Publications, 1965

[4]Chien-Hsun Lu, Exploring Steiner’s Proism with Cabir Geometry. Author’s homepage: http://home.educities.edu.tw/iamalumi/