NoDI seminar

Geometric construction problems and invariance

Pascal Schreck 15:00, January 29, 2015 321 Main Building, Beihang University

Abstract: Nowadays, geometric constructions are mainly considered in the domain of education whereas the professional occupations where they were traditionally used, like land surveyor or engineering draughtsman, take now advantage of the ability of computers to make complex calculations. Anyway, if we come back to these ancient days when tees, compass and drawing boards were the only instruments in use, construction problems coming from engineering were very similar to those considered in mathematics. All these problems share the same interesting feature:  they are invariant under the action of direct isometries (also called rigid body motions). In this talk, I will first recall some basic facts about geometric constructions, and particularly straightedge and compass constructions, through some simple examples. I will also make a small detour through algebra via Wu's method and Galois theory.    Then, I will expose the basic techniques used in CAD for decomposing construction problems. These techniques often mix elements of rigidity theory and counting of unknowns and equations on a so-called graph of constraints. I will show that not only the direct isometry group can be used  but also translation group or similarity group.    Finally, in the light of the previous points, I will discuss some relations between geometric constructions and proofs in geometry.

Poster Slides Photos