On the Mechanization of Straightedge and Compass Constructions Pascal Schreck To cite this version: Pascal Schreck. On the Mechanization of Straightedge and Compass Constructions. Journal of Sys- tems Science and Complexity, Springer Verlag (Germany), 2019, 32 (1), pp.124-149. 10.1007/s11424- 019-8347-1. hal-02485474 HAL Id: hal-02485474 https://hal.archives-ouvertes.fr/hal-02485474 Submitted on 20 Feb 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Noname manuscript No. (will be inserted by the editor) On the Mechanization of Straightedge and Compass Constructions Pascal Schreck the date of receipt and acceptance should be inserted later E-mail:
[email protected] Abstract The geometric constructions obtained with only straightedge and com- pass 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.