Last Edited 18 December 2012 by klobuch2@illinois.edu

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Math 198 Fall 2012

The purpose of Cliffhopf is to model the stereographic projection of the Clifford Torus doing a 4th dimensional rotation, as in Tom Banchoff's movie on the Hypertorus, of which parts may be viewed here. After first being modelled with DPGraph, this Clifford Torus is modeled using the PyOpenGL library. |

A torus is created by revolving a circle in the 3rd dimension around a circle, which is why a torus is a "surface of revolution." The Clifford Torus is a special kind of torus (a doughnut shaped surface) in the 4th dimension. It splits a 4th dimensional sphere in half; it is the latitude of the hypersphere. Much like a duocylinder, it is the product of two Cartesian circles. You can find a more geometrical definition of the Clifford Torus here. |

The purpose of this project was to model the Clifford Torus, with hope of creating a viable CUBE program. It began in DPGraph, using the parametric equations found on Wikipedia.org, pictured here below.
From that equation, using the coordinates (x
The code for the DPGraph program can be found here.
Here is a PDF of my final presentation. |