After discussing some well-known examples in geometry and function theory, we study surfaces in space that are defined by the vanishing of the torsion of integral curves of a given vector field.
KeywordsVector Field Space Curve Ricci Flow Space Curf Lorenz Attractor
I first started using iterated exponentiation to illustrate bifurcation in a project for a Maple course I taught in Oxford in the 1990s. Remnants of this course are available on my homepage.
The study of space curves with assigned torsion and curvature is described in , and I used it as a student competition to find an interesting space curve by guessing simple candidate functions in a differential geometry course in Turin.
The vector field Q a is the basis of the author’s animation
Figure 25 arises from the vector field (4) with cubic components. As personal computing power increases, it will be easier to study more and more complicated vector fields and their associated surfaces.
The ESMA conference taught me not just to better appreciate artistic aspects inherent in modern mathematics, and but also the importance of explaining to a wider public the underlying geometrical ideas I deal with on a daily basis. I found myself having to work on a number of deep mathematical problems to answer some of the questions that arose. In this respect, I wish to express gratitude to the participants, and in particular François Apery, Claude Bruter, Eugenia Emets, George Hart, and Jos Leys. Thanks are also due to Claude for his afternoon visits from Gometz to Bures encouraging me to finish the text.
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