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Integrating dynamic geometry software, deduction systems, and theorem repositories. (English) Zbl 1188.68264

Borwein, Jonathan M. (ed.) et al., Mathematical knowledge management. 5th international conference, MKM 2006, Wokingham, UK, August 11–12, 2006. Proceedings. Berlin: Springer (ISBN 3-540-37104-4/pbk). Lecture Notes in Computer Science 4108. Lecture Notes in Artificial Intelligence, 280-294 (2006).
Summary: 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.
For the entire collection see [Zbl 1114.68004].

MSC:

68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
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