On the Mechanization of Straightedge and Compass Constructions  

作　　者：SCHRECK Pascal 

机构地区：[1]Université de Strasbourg, UFR de Mathématique et Informatique-ICube

出　　处：《Journal of Systems Science & Complexity》2019年第1期124-149,共26页系统科学与复杂性学报（英文版）

基　　金：supported by Strasbourg University and French CNRS

摘　　要：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 ?gures 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.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 ?gures 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.

关 键 词：Geometric KNOWLEDGE-BASED systems regular CHAINS straightedge and COMPASS constructibility TRIANGLE problems Wu's method 

分 类 号：O1[理学—数学]