1. Dynamiser la géométrie élémentaire: introduction à des travaux de Richard Schwartz
- Author
-
Marcel Berger
- Subjects
iteration of geometric transformations ,barycentric subdivisions ,euclidean and projective shapes of polygons ,projective geometry ,cross ratio ,pappus theorem ,desargues theorem ,pentagram map ,recurrence theorem ,dynamical systems ,poncelet polygons ,Mathematics ,QA1-939 - Abstract
In some recent works in various situations Richard Schwartz has studied the following type of problem: starting with a given type of a geometric figure P one applies to it a geometric operation f to get a new figure f(P). Now when one iterates that process one gets a infinite series of figures f n(P) . The question is to study this discrete dynamical system. Using computers to guess results, then Schwartz succeeds in getting (mathematically) nice theorems, but also this leads him to various open problems and conjectures. In the present text we present what Schwartz did in four of these situations.
- Published
- 2005