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球面上圓的性質
Thesis

球面上圓的性質

李函燊
Masters, 國立清華大學, 數學系
2011

Abstract

球面上的圓
My goal is to discover some properties of circles on sphere by inversing some circle theorems on the plane in some sphere, i.e. their stereographic projection respect to some sphere. Since all the graphics lie on the same plane, they will lie on the same ball after inversing to a sphere. And the inversion of a circle is still a circle. Hence, we will obtain some circles on sphere. Then we exam whether it keeps the original properties or generates some new properties. Therefore we will start to construct graphics on the plane first then there should be no difficulties to construct theorems in space. We use Cabri II and Cabri 3D as convenient tools to discover geometric properties. In this article we will discuss about Soddy Circles and Seven Circles Theorem.

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