Integrating Dynamic Geometry Software, Deduction Systems, and Theorem Repositories

Quaresma, Pedro; Janicic, Predrag

doi:10.1007/11812289_22

Cited by 12 publications

(15 citation statements)

References 6 publications

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“…Both this types are suitable for our purpose of building an e-course for learning formal reasoning in geometry, in the following we will focus in the ATP that one of the authors worked on, the GCLCPROVER Quaresma & Janičić, 2006a), which is based in the area method. In either case the geometrical ATPs can be used, in a very fruitful way, in the learning process Quaresma & Janičić, 2006b). In the following we will present two different uses of the ATPs in geometry, showing some examples of application of existing software tools.…”

Section: Automatic Theorem Proving In Geometrymentioning

confidence: 99%

“…To build what we call an adaptative learning environment for geometry, we have to integrate the DGSs the ATPs and a repository of problems in a LMS in order to build an environment where the student can have a broad experimental, but with a strong formal support, learning platform. Such an integration it is still to be done, there are already many excellent DGSs, some of them have some sort of integration with ATPs, others with RGP (Quaresma & Janičić, 2006b;, some attempts to integrate this tools in a LMS have already been done (Santos & Quaresma, 2008), but, as far as we know, all this integrations are partial integrations. A system where all this tools are integrated and can be used in a fruitful fashion does not exist yet.…”

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confidence: 99%

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Adaptative Learning Environment for Geometry

Santos¹,

Quaresma²

2010

Advances in Learning Processes

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Section: Automatic Theorem Proving In Geometrymentioning

confidence: 99%

mentioning

confidence: 99%

Adaptative Learning Environment for Geometry

Santos¹,

Quaresma²

2010

Advances in Learning Processes

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“…More details on storing mathematical contents and other mathematical knowledge management aspects of the gcl language and its processors are discussed in [30].…”

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confidence: 99%

“…For example, C.a.R. 30 has support for hyperbolic and elliptic geometry. Cinderella.2 has native support for projective and hyperbolic geometry, but also provides an environment for doing interactive physics experiments.…”

mentioning

confidence: 99%

Geometry Constructions Language

Janicic

2009

J Autom Reasoning

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Geometry Constructions Language (gcl) is a language for explicit descriptions of constructions in Euclidean plane and of their properties. Other mathematical objects can also be described in the language. The language gcl is intuitive and simple, yet it supports arrays, flow control structures, user-defined procedures, etc. The processors for the gcl language -applications gclc and Wingclc-enable visualization of described objects and producing of mathematical illustrations, provide different semantical information and support for automated proving of properties of the constructed objects. These features make the tools gclc and Wingclc powerful mechanized geometry systems and they have thousands of users worldwide.

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“…Our system is implemented within dynamic geometry software GCLC [11] and Eukleides [19,23] and uses a geometry theorem prover, GCLCprover [12], based on the area method [4,5]. Our framework, GeoThms [21,22], is a Web tool that integrates the above components with a repository of theorems related to geometric constructions.…”

Section: Introductionmentioning

confidence: 99%

Automatic Verification of Regular Constructions in Dynamic Geometry Systems

Janicic

Quaresma

Automated Deduction in Geometry

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Abstract. We present an application of automatic theorem proving (ATP) in the verification of constructions made with dynamic geometry software (DGS). Given a specification language for geometric constructions, we can use its processor to deal with syntactic errors. The processor can also detect semantic errors -situations when, for a given concrete set of geometrical objects, a construction is not possible. However, dynamic geometry tools do not test if, for a given set of geometrical objects, a construction is geometrically sound, i.e., if it is possible in a general case. Using ATP, we can do this last step by verifying the geometric constructions deductively. We have developed a system for the automatic verification of regular constructions (made within DGSs GCLC and Eukleides), using our ATP system, GCLCprover. This gives a real-world application of ATP in dynamic geometry tools.

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Integrating Dynamic Geometry Software, Deduction Systems, and Theorem Repositories

Cited by 12 publications

References 6 publications

Adaptative Learning Environment for Geometry

Adaptative Learning Environment for Geometry

Geometry Constructions Language

Automatic Verification of Regular Constructions in Dynamic Geometry Systems

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