3D Poncelet Porism and Steiner Porism

Jen-chung Chuan

 http://sylvester.math.nthu.edu.tw/d2/atcm09/3D%20Poncelet%20Proism%20and%20Steiner%20Porism.htm

Abstract

The plane version of the various forms of the Poncelet porism and Steiner porism has been experimented with Cabri Java Applets:

http://poncelet.math.nthu.edu.tw/disk3/cabrijava/index.htm

Here we wish to extend the analogous phenomena in 3D. In this workshop we are to explore the mathematical properties with the Cabri 3D files prepared before-hand:

 

1)     Inversion of Circles Inscribed in Faces of Pentagonal Cupola:

 

2) Poncelet Porism for Escribed-Inscribed Quadrilaterals:

 

3) Poncelet Porism for Quadrilaterals:

4) Sphere Inversion:

5. Steiner Porism on Sphere:

6) Inversion of Circles Inscribed in Faces of Cuboctahedron:

 

7) Inversion of Circles Inscribed in Faces of Cuboctahedron II:

 

8) Inversion of Circles Inscribed in Faces of Square Cupola:

9) Inversion of Circles Inscribed on Faces of Dodecahedron:

 

Software environment: Cabri 3D installed in Windows XP. Network connection will enhance the demo but is not required.