Techniques for visualizing Fermat's last theorem: a case study

摘要

The authors describe some mathematical approaches and computer graphics techniques for illustrating concepts related to Fermat's last theorem. They present a selection of visualization methods, and describe observations made in the process of creating a three-minute computer animated videotape dealing with some elementary aspects of Fermat's last theorem, a problem in number theory. The approach to the representation of the different concepts presented in the video was influenced by many factors: the available hardware, real and perceived constraints of the available software, constraints imposed by the video medium, and a number of peculiarities and features of the mathematical domain itself. The authors describe the experiences with the software systems that played a part in these efforts, some specific successful visualization techniques, and some unexpected mathematical insights.