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Mathematics in Computer Science

, Volume 10, Issue 1, pp 41–56 | Cite as

Automatic Constructibility Checking of a Corpus of Geometric Construction Problems

  • Pascal Schreck
  • Pascal Mathis
Article

Abstract

Straightedge and compass constructions play a special role in geometry. First, for a very long time, they were used in practice by land surveyors or architects in order to solve concrete problems. Second, they are an inexhaustible source of exercises used to learn concepts in geometry. And finally, some famous impossible problems related to straightedge and compass constructions waited centuries before being solved using algebra. In addition, not knowing if a well-constrained problem is constructible with straightedge and compass or not, make that kind of problems more difficult to address: should we synthesize a program or on the contrary find a counterexample has to be found and treated using algebra or reduction on it? In this paper, we perform a systematic checking of a whole corpus of problems proposed by William Wernick. We expose our methodology and the algorithm we used. For each problem, its constructibility status is computed and either an algebraic argument or a geometric construction is given.

Keywords

Straightedge and compass constructions Regular chains Galois theory Wernick’s list 

Mathematics Subject Classification

Primary 51-04 Secondary 97G99 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.ICube, UMR CNRS 7357Université de StrasbourgStrasbourgFrance

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