The Mathematica Journal
Volume 11, Issue 3

Search

In This Issue
Articles
Mathematica Resources

Download This Issue 

About the Journal
Editorial Policy
Staff and Contributors
Submissions
Back Issues
Contact Information

On the Visualization of Riemann Surfaces
Simo Kivelä

The graphs of complex-valued functions f:C -> C or functions of the type f:R^2 -> R^2 are in general two-dimensional manifolds in the space R^4. The article presents a method for the visualization of such a graph. The graph is first projected to three-dimensional space with parallel projection and the image—the surface in three-dimensional space—is rendered on the screen in the usual way. The visualization can be improved in two ways: the graph can be rotated in four-dimensional space or the direction line of the projection can be changed, which means that the observer flies around the graph in four dimensions. The animation and manipulation capabilities of Mathematica are appropriate tools for the purpose.

*Notebook


*PDF


About the Author
Simo K. Kivelä is an emeritus lecturer of mathematics. He has used mathematical software like muMath, Matlab, and Mathematica in several courses, beginning in the 1970s. He has also been the supervisor of projects where information and communication technologies are used in teaching and studying mathematics. He has continued this work as a part-time researcher after retirement.

Simo Kivelä
Helsinki University of Technology,
Institute of Mathematics,
P.O. Box 1100,
FI-02015 HUT, Finland

simo.kivela@tkk.fi


     
About Mathematica | Download Mathematica Player
© 2010 Wolfram Media, Inc. All rights reserved.