Abstract

Classical mechanics can be formalized using Euclidean geometry (the one we learn at school, with Pythagorean’s theorem, similar triangles, etc). In such a world light travels along straight lines as these paths are the one minimizing their travel time. Since the 19th century mathematicians have created and studied new geometrical “worlds” where the axioms of Euclidean geometry no longer hold. These geometries have been a source of inspiration for some artists such as M. C. Escher, who drew remarkable pictures of the hyperbolic space in two dimensions. Using the power of modern computers, one can now simulate what it would be to live an a non-Euclidean three-dimensional space. In such a world light rays may bend, thus changing our large-scale perception of the surrounding space. The talk will be a journey in these non-Euclidean geometries.