Sébastien Gandon – Indoor geometry: On the tradition of construction with obstructions in the plane
The Montreal Inter-University Workshop on the History and Philosophy of Mathematics presents:
Sébastien Gandon (Clermont-Ferrand)
Indoor geometry: On the tradition of construction with obstructions in the plane
Wednesday, February 16, 2011, 5:00-7:00pm
McGill University, Leacock Building, Room 927.
Abstract: In order to prove a geometric theorem, one often has to extend the lines and to introduce new points in the given figure. But, what to do if the sheet of paper on which one does the constructions is too small to encompass the extensions? The obvious answers are: “do it again”, “take this problem into consideration when beginning your drawing”, “take a larger sheet of paper” or “draw a smaller figure”.
However, there is—and has been—another answer, which consists in attempting to prove the theorem without going over the edge of the sheet of paper. In this talk, I will speak about this tradition of geometrical constructions “with obstructions in the plane”. I will claim that it has a long history (one finds some trace of it in Proclus and Hero of Alexandria), and that it always has a double dimension: practical, on the one hand, and foundational, on the other (how to reconcile the infinity of Euclidean space with the finitude of the heavens?). I will secondly claim that this sort of issue has played a very important role in the foundational discussions concerning the nature of projective space in Klein and Pasch.
For more information, please contact:
Gregory Lavers (Concordia), Mathieu Marion (UQÀM), Jean-Pierre Marquis (UdM), Dirk Schlimm (McGill).