On the Mechanization of Straightedge and Compass Constructions

Pascal Schreck (1)

1 LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection

The geometric constructions obtained with only straightedge and compass are famous and play a special role in the development of geometry. On the one hand, the constructibility of figures is a key ingredient in Euclid geometry and, on the other hand, unconstructibility gave birth to famous open problems of the ancient Greece which were unlocked only in the nineteenth century using discoveries in algebra. This paper discusses the mechanization of straightedge and compass constructions. It focuses on the algebraic approaches and presents two methods which are implemented; one is due to Lebesgue and the other one was jointly designed by Gao and Chou. Some links between the algebraic approach of constructions and synthetic geometry are described.

Mots clés: Straightedge and compass constructibility; triangle problems; geometric knowledge-based systems; Wu's method; regular chains

Domaines: Logique en informatique [cs.LO]; Informatique [cs]; Calcul formel [cs.SC]

Pascal Schreck. On the Mechanization of Straightedge and Compass Constructions. Journal of Systems Science and Complexity, 2019, 32 (1), pp.124-149. ⟨10.1007/s11424-019-8347-1⟩. ⟨hal-02485474⟩