The Mathematica Journal
Departments
Feature Articles
Columns
New Products
New Publications
Classifieds
Calendar
News Bulletins
Mailbox
Letters
FAQ
Write Us
About the Journal
Staff and Contributors
Submissions
Subscriptions
Advertising
Back Issues
Home
Download this Issue

Experiments in the Theory of Surfaces

Yoshihiko Tazawa
Tokyo Denki University
tazawa@cck.dendai.ac.jp

The purpose of this article is to show the advantage of using Mathematica in the theory of surfaces. The examples in the classical differential geometry, namely the theory of curves and surfaces, have been confined to a small group of calculable objects, because of the difficulty in evaluating geometrical quantities and solving differential equations explicitly. But Mathematica has made it possible to deal with a wide range of objects and to perform experimental treatments of them, based on the power of numerical calculation--the NDSolve and NIntegrate commands in particular--and graphical visualization by the ParametricPlot command. I would like to introduce here several animations and figures that I use in my differential geometry class for undergraduate students. First of all, these graphics help students understand the basic notions of differential geometry. Secondly, we can experiment on geometry through these graphics. This article is one of the serial talks given by the author at 1995 Developer Conference, IMS '97 in Rovaniemi, and WMC 98 in Chicago. They are all targeted for the experimental usage of Mathematica on differential geometry. This time the topics are focused on the surfaces in the three-dimensional Euclidean space. The commands are contained in six notebooks. If the commands in other notebooks cause any trouble, please restart Mathematica. See also the explanation of the notebooks.

south.rotol.ramk.fi/~keranen/IMS99/paper37/ims99paper37.html


Copyright © 2001 Wolfram Media, Inc. All rights reserved.

[Article Index][Prev Page][Next Page]