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Integrating Dynamic Geometry Software, Deduction Systems, and Theorem Repositories

  • Pedro Quaresma
  • Predrag Janičić
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4108)

Abstract

The axiomatic presentation of geometry fills the gap between formal logic and our spatial intuition. The study of geometry is, and will always be, very important for a mathematical practitioner. GCLCprover, an automatic theorem prover (ATP) integrated with dynamic geometry software (DGS) gives its user a tool to bridge his/her spatial intuition with formal, Euclidean geometry proofs. GeoThms, a system consisting of the mentioned programs and a database geoDB, provides a framework for exploring geometrical knowledge. A GeoThms user can browse through a list of available geometric problems, their statements, illustrations, and proofs. He/she can also interactively produce new geometrical constructions, theorems, and proofs and add new results to the existing ones. GeoThms framework provides an environment suitable for new ways of studying and teaching geometry at different levels. GeoThms also provides a system for storing mathematical knowledge (in a explicit, declarative form) — not only theorem statements, but also their (automatically generated) proofs and corresponding illustrations.

Keywords

Mathematical Knowledge Theorem Prover Geometric Construction Regular User Area Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Pedro Quaresma
    • 1
  • Predrag Janičić
    • 2
  1. 1.Department of MathematicsUniversity of CoimbraCoimbraPortugal
  2. 2.Faculty of MathematicsUniversity of BelgradeBelgradeSerbia & Montenegro

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