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On Protocols for the Automated Discovery of Theorems in Elementary Geometry

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Abstract

In this paper we consider the problem of dealing automatically with arbitrary geometric statements (including, in particular, those that are generally false) aiming to find complementary hypotheses for the statements to become true. Our approach proceeds within the framework of computational algebraic geometry. First we argue and propose a plausible protocol for automatic discovery, and then we present some algorithmic criteria, as well as the meaning (regarding the algebraic geometry of the varieties involved in the given statement), for the protocol success/failure. A detailed collection of examples in also included.

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Authors and Affiliations

  1. University of Pisa, Largo Pontecorvo 5, Pisa, Italy

    G. Dalzotto

  2. Universidad de Cantabria, Avda. Los Castros, Santander, Spain

    T. Recio

Authors
  1. G. Dalzotto
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  2. T. Recio
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Correspondence to T. Recio.

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Last author supported by grant “Algoritmos en Geometría Algebraica de Curvas y Superficies” (MTM2008-04699-C03-03) from the Spanish MICINN.

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Dalzotto, G., Recio, T. On Protocols for the Automated Discovery of Theorems in Elementary Geometry. J Autom Reasoning 43, 203–236 (2009). https://doi.org/10.1007/s10817-009-9133-x

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  • DOI: https://doi.org/10.1007/s10817-009-9133-x

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