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Journal of Systems Science and Complexity

, Volume 32, Issue 1, pp 124–149 | Cite as

On the Mechanization of Straightedge and Compass Constructions

  • Pascal SchreckEmail author
Article

Abstract

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.

Keywords

Geometric knowledge-based systems regular chains straightedge and compass constructibility triangle problems Wu’s method 

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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Université de Strasbourg, UFR de Mathématique et Informatique - ICubeStrasbourgFrance

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