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Determining automatically compass and straightedge unconstructibility in triangles

13 pagesPublished: March 27, 2016


In many areas, some geometry problems can not be solved using only geometry and are treated by the means of algebraic tools. However, geometric properties can be still employed to simplify the system of equations. This allows either to speed up the treatment or, more radically, to make the treatment possible. In this article we illustrate this approach with a family of toy examples. In all these problems the goal it is to determine if there is a compass-and-straightedge construction of the three vertices of a triangle knowing only three located points of this triangle. Algebraic tools, basically Galois theory, are needed to answer the question. But in many cases a geometric reasoning phase is required to provide a polynomial algebraic system that algebraic softwares can address within a acceptable time despite the exponential complexity of the underlying algorithms.

Keyphrases: automated reasoning, Compass and straightedge construction, symbolic computation

In: James H. Davenport and Fadoua Ghourabi (editors). SCSS 2016. 7th International Symposium on Symbolic Computation in Software Science, vol 39, pages 130--142

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