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Title

UmlaufSatz Movie
Author

Yoshihiko Tazawa
Organization: Tokyo Denki University
Department: Natural Sciences
Conference

2003 International Mathematica Symposium
Conference location

Imperial College, London
Description

At IMS2001, I gave a presentation titled "Gauss-Bonnet Theorem by Mathematica." It contained a visualization of the elegant proof of the Umlaufsatz (Theorem of Turning Tangents) by Heinz Hopf, mainly using still figures [1]. In this talk I will show full animations of figures of the detailed proof, incorporated into a movie. Visualizing proofs, and visualizing through computer graphics in particular, gives viewers clear images of the situation, but at the same time it can give some slanted points of view. In this movie I tried to show as many figures as possible to avoid a loss in generality, tracing the figures we imagine in our mind when we follow the proof.
Subjects

*Mathematica Technology > Programming > Animations
*Mathematics > Geometry > Computational Geometry
Keywords

Umlaufsatz, Theorem of Turning Tangents, full animations, movie, visualizing proofs, computer graphics
Related items

*Challenging the Boundaries of Symbolic Computation: Proceedings of the 5th International Mathematica Symposium   [in Books]