Abstract / résuméCUMC / CCEM 2005



Name / nom: François Bolduc

School / école: Université Laval

Length / durée: 50 min

Title / titre: Geometrical Construction and Its Famous Problems

Abstract / résumé: The ABC of geometrical constructibility with a ruler and a compass: introduction to the Euclidian (read tedious) methods of ruler and compass constructions, along with the basic tricks underlying. An overview of the "constructible" Euclidian plane through field extensions with the constructions done beforehand. Then I will attack the "classic" problems of Euclidian geometry: the duplication of the cube, the trisection of an angle, squaring the circle and constructing regular polygons inside a given circle, or with a given side length. The first three are indeed impossible, unless you cheat your Euclidian plane.

Prerequisites / choses nécessaires: I assume the audience to know more algebra than geometry, but will not assume more advanced algebra than basic knowledge of field structure and some vague intuition about how to extend one - for instance from R to C - in a finite manner. Also, I will not assume any geometry knowledge (though the basics will be dealt with swiftly).



PDF format / format PDF: bolduc.pdf