# System Description: GCLCprover + GeoThms

### Authors

### Abstract

Dynamic geometry tools (e.g., "Cinderella", "Geometer's Sketchpad", "Cabri", "Eukleides" visualise geometric objects, allow interactive work, and link formal, axiomatic nature of geometry (most often --- Euclidean) with its standard models (e.g., Cartesian model) and corresponding illustrations. These tools are used in teaching and studying geometry, some of them also for producing digital illustrations. The common experience is that dynamic geometry tools significantly help students to acquire knowledge about geometric objects. However, despite the fact that geometry is an axiomatic theory, most (if not all) of these tools concentrate only on concrete models of some geometric constructions and not on their abstract properties --- their properties in deductive terms. The user can vary some initial objects and parameters and test if some property holds in allchecked cases, but this still does not mean that the given property is valid.

We have extended GCLC, a widely used dynamic geometry package, with a module that allows formal, deductive reasoning about constructions made in the main, drawing module. The built-in theorem prover (GCLCprover in the following text), is based on the area method. It produces proofs that are human-readable (in LaTeX form), and with a justification for each proof step. It is also possible, via a conversion tool, to reason

about constructions made with Eukleides. Hence, the prover can be used in conjunction with other dynamic

geometry tools, which demonstrates the flexibility of the developed deduction module. Closely linked to the mentioned tools is GeoThms --- a web tool that integrates dynamic geometry tools, geometry theorem provers, and a repository of geometry theorems and proofs. This integrated framework for constructive geometry, provides an environment suitable for new ways of studying and teaching geometry at different levels.

### Keywords

Dynamic Geometry Software, Automatic Theorem Proving, Geometry### Subject

Automated theorem proving### Conference

3rd International Joint Conference on Automated Reasoning 3rd International Joint Conference on Automated Reasoning, August 2006### Cited by

#### Year 2015 : 3 citations

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#### Year 2014 : 1 citations

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#### Year 2013 : 1 citations

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#### Year 2012 : 3 citations

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#### Year 2011 : 1 citations

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#### Year 2010 : 3 citations

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