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Towards Understanding Triangle Construction Problems

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Intelligent Computer Mathematics (CICM 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7362))

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Abstract

Straightedge and compass construction problems are one of the oldest and most challenging problems in elementary mathematics. The central challenge, for a human or for a computer program, in solving construction problems is a huge search space. In this paper we analyze one family of triangle construction problems, aiming at detecting a small core of the underlying geometry knowledge. The analysis leads to a small set of needed definitions, lemmas and primitive construction steps, and consequently, to a simple algorithm for automated solving of problems from this family. The same approach can be applied to other families of construction problems.

This work was partially supported by the Serbian Ministry of Science grant 174021 and by Swiss National Science Foundation grant SCOPES IZ73Z0_127979/1.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, University of Belgrade, Serbia

    Vesna Marinković & Predrag Janičić

Authors
  1. Vesna Marinković
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  2. Predrag Janičić
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Editor information

Editors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University and Open Universiteit Nederland, Princetonplein 5, 3584 CC, Utrecht, The Netherlands

    Johan Jeuring

  2. Department of Computer Science, University College London, Gower Street, WC1E 6BT, London, UK

    John A. Campbell

  3. Department of Computing and Software, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    Jacques Carette

  4. Department of Computer Science and Engineering, Texas A&M University, 77843-3112, College Station, TX, USA

    Gabriel Dos Reis

  5. Department of Computer Graphics and Design, Masaryk University, Botanická 68a, 60200, Brno, Czech Republic

    Petr Sojka

  6. Laboratoire de Recherche en Informatique (LRI - UMR8623) PCRI, Université Paris-Sud, Batiment 650, 91405, Orsay Cedex, France

    Makarius Wenzel

  7. The University of Birmingham, School of Computer Science,, B15 2TT, Edgbaston, Birmingham, UK

    Volker Sorge

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Marinković, V., Janičić, P. (2012). Towards Understanding Triangle Construction Problems. In: Jeuring, J., et al. Intelligent Computer Mathematics. CICM 2012. Lecture Notes in Computer Science(), vol 7362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31374-5_9

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  • DOI: https://doi.org/10.1007/978-3-642-31374-5_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31373-8

  • Online ISBN: 978-3-642-31374-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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