The problem? Although such a transformation had been proved to exist, no one could actually visualize it. In this documentary, Geoffroy and Dominique Garing follow Vincent Borelli and his team, who are determined to produce a visualization of this geometric feat. They embark on a major project combining computing, geometry and visualization to move the science forward and shed light on something that had long remained opaque. Through a wealth of archival footage and in-depth interviews with everyone involved, the documentary takes us through every twist and turn of this remarkable adventure, from the initial question (why had no one ever created an image of this torus?) to the moment the champagne bottle is opened. Contributions from Cédric Villani and "mini-lessons" by Étienne Ghys feature throughout the documentary, helping everyone grasp the meaning of each term. The conversations range over the hypotheses of the theorems, the transition from the abstract to the concrete, the distinction between the existence of an example and actually exhibiting one, and much more. Finally, the film culminates in a magnificent video of the famous torus, revealing an example of a smooth fractal—a new family of objects to explore.
The flat torus saga: a documentary | Tangente
The saga of the flat torus
Have you heard of smooth fractals? The story began in the early 1950s, when John Nash astonished everyone by proving that a square could be gently warped into a torus without folding, creasing, stretching or contracting it in ways that alter lengths.
