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The Area Method

A Recapitulation

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Abstract

The area method for Euclidean constructive geometry was proposed by Chou, Gao and Zhang in the early 1990’s. The method can efficiently prove many non-trivial geometry theorems and is one of the most interesting and most successful methods for automated theorem proving in geometry. The method produces proofs that are often very concise and human-readable. In this paper, we provide a first complete presentation of the method. We provide both algorithmic and implementation details that were omitted in the original presentations. We also give a variant of Chou, Gao and Zhang’s axiom system. Based on this axiom system, we proved formally all the lemmas needed by the method and its soundness using the Coq proof assistant. To our knowledge, apart from the original implementation by the authors who first proposed the method, there are only three implementations more. Although the basic idea of the method is simple, implementing it is a very challenging task because of a number of details that has to be dealt with. With the description of the method given in this paper, implementing the method should be still complex, but a straightforward task. In the paper we describe all these implementations and also some of their applications.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000, Belgrade, Serbia

    Predrag Janičić

  2. LSIIT, UMR 7005 CNRS-ULP, University of Strasbourg, Pôle API, Bd Sébastien Brant, BP 10413, 67412, Illkirch, France

    Julien Narboux

  3. CISUC, Department of Mathematics, University of Coimbra, 3001-454, Coimbra, Portugal

    Pedro Quaresma

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  1. Predrag Janičić
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  2. Julien Narboux
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  3. Pedro Quaresma
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Correspondence to Pedro Quaresma.

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The first author is partially supported by the grant 144030 of the Ministry of Science of Serbia. The second author is partially supported by the ANR project Galapagos.

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Janičić, P., Narboux, J. & Quaresma, P. The Area Method. J Autom Reasoning 48, 489–532 (2012). https://doi.org/10.1007/s10817-010-9209-7

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