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Mathematics in Computer Science

, Volume 10, Issue 1, pp 5–25 | Cite as

On the Unavoidable Uncertainty of Truth in Dynamic Geometry Proving

Article

Abstract

The aim of this note is to discuss some issues posed by the emergency of universal interfaces able to decide on the truth of geometric statements. More specifically, we consider a recent GeoGebra module allowing general users to verify standard geometric theorems. Working with this module in the context of Varignon’s theorem, we were driven—by the characteristics of the GeoGebra interface—to perform a quite detailed study of the very diverse fate of attempting to automatically prove this statement, when using two different construction procedures. We highlight the relevance—for the theorem proving output—of expression power of the dynamic geometry interface, and we show that the algorithm deciding about the truth of some—even quite simple—statements can fall into a not true and not false situation, providing a source of confusion for a standard user and an interesting benchmark for geometers interested in discovering new geometric facts.

Keywords

Dynamic geometry Automated theorem proving GeoGebra Varignon theorem 

Mathematics Subject Classification

Primary 68T15 Secondary 68W30 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Depto. de Matemática Aplicada IUniversity of Vigo, EE ForestalPontevedraSpain
  2. 2.Depto. de Matemáticas, Estadística y ComputaciónUniversity of CantabriaSantanderSpain

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