Meanders: A personal perspective to the memory of Pierre Rosenstiehl

Abstract

 J’errais dans un méandre ;  J’avais trop de partis,  Trop compliqués, à prendre...  (Edmond Rostand,  Cyrano de Bergerac)

Meander is a self-avoiding closed curve on a plane which intersects a straight line in a given set of points. Meander is a very simple object. In the elementary school, we may ask children to draw a few meanders and to admire their strange beauty. In the middle school, we may ask children to perform an exhaustive search of the meanders with a small number of intersections with the line. Then, gradually, we start to perceive an incredible profoundness of the subject, whose relations go from enumeration to quantum field theory and string theory. Pierre Rosenstiehl was one of the pioneers in the study of the algorithmic aspects of meanders, and he also was a passionate connoisseur of labyrinths, of which the meanders are a particular case.