Adding remote computational capabilities to Dynamic Geometry Systems

Escribano, Jesús; Botana, Francisco; Abánades, Miguel A.

doi:10.1016/j.matcom.2008.04.019

Cited by 11 publications

(8 citation statements)

References 7 publications

(11 reference statements)

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“…The geometric construction, object of the query, is equal or a subfigure of those figures. 7 The first version of the geometric semantic search mechanism is already implemented in TGTP, using the GeoGebra JavaScript applet for building the geometric query. The proposed geometric (semantic) search mechanism implemented in TGTP works as follows:…”

Section: Searching For Geometric Informationmentioning

confidence: 99%

Exchange of Geometric Information Between Applications

Quaresma

Santos

Baeta

2018

Electron. Proc. Theor. Comput. Sci.

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The Web Geometry Laboratory (WGL) is a collaborative and adaptive e-learning Web platform integrating a well known dynamic geometry system. Thousands of Geometric problems for Geometric Theorem Provers (TGTP) is a Web-based repository of geometric problems to support the testing and evaluation of geometric automated theorem proving systems.The users of these systems should be able to profit from each other. The TGTP corpus must be made available to the WGL user, allowing, in this way, the exploration of TGTP problems and their proofs. On the other direction TGTP could gain by the possibility of a wider users base submitting new problems.Such information exchange between clients (e.g. WGL) and servers (e.g. TGTP) raises many issues: geometric search-someone, working in a geometric problem, must be able to ask for more information regarding that construction; levels of geometric knowledge and interest-the problems in the servers must be classified in such a way that, in response to a client query, only the problems in the user's level and/or interest are returned; different aims of each tool-e.g. WGL is about secondary school geometry, TGTP is about formal proofs in semi-analytic and algebraic proof methods, not a perfect match indeed; localisation issues, e.g. a Portuguese user obliged to make the query and process the answer in English; technical issues-many technical issues need to be addressed to make this exchange of geometric information possible and useful.Instead of a giant (difficult to maintain) tool, trying to cover all, the interconnection of specialised tools seems much more promising. The challenges to make that connection work are many and difficult, but, it is the authors impression, not insurmountable.

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Section: Searching For Geometric Informationmentioning

confidence: 99%

Exchange of Geometric Information Between Applications

Quaresma

Santos

Baeta

2018

Electron. Proc. Theor. Comput. Sci.

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“…Thus, the approach attracted the attention of developers, being this approach behind the LocusEquation command in the current version of GeoGebra 3 . Furthermore, it has also been implemented by the DG system JSXGraph using remote computations on a server [31], an idea previously developed in [32].…”

Section: Locus Discovery With Algebraic Elimination Techniquesmentioning

confidence: 99%

An algebraic taxonomy for locus computation in dynamic geometry

Abánades¹,

Botana²,

Montes³

et al. 2014

Computer-Aided Design

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The automatic determination of geometric loci is an important issue in Dynamic Geometry. In Dynamic Geometry systems, it is often the case that locus determination is purely graphical, producing an output that is not robust enough and not reusable by the given software. Parts of the true locus may be missing, and extraneous objects can be appended to it as side products of the locus determination process. In this paper, we propose a new method for the computation, in dynamic geometry, of a locus defined by algebraic conditions. It

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“…This same algorithm has recently been implemented by the DGS JSXGraph to determine the equation of a locus set using remote computations on a server [22], an idea previously developed by the authors in [17].…”

Section: Automatic Discovery and Locus Equationsmentioning

confidence: 99%

Automatic deduction in (dynamic) geometry: Loci computation

Botana

Abánades

2014

Computational Geometry

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A symbolic tool based on open source software that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction is presented. The prototype has been developed as two different worksheets for the open source computer algebra system Sage, corresponding to two different ways of coding a geometric construction, namely with the open source dynamic geometry system GeoGebra or using the common file format for dynamic geometry developed by the Intergeo project. Locus computation algorithms based on Automatic Deduction techniques are recalled and presented as basic for an efficient treatment of advanced methods in dynamic geometry. Moreover, an algorithm to eliminate extraneous parts in symbolically computed loci is discussed. The algorithm, based on a recent work on the Gröbner cover of parametric systems, identifies degenerate components and extraneous adherence points in loci, both natural byproducts of general polynomial algebraic methods. Several examples are shown in detail.

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Adding remote computational capabilities to Dynamic Geometry Systems

Cited by 11 publications

References 7 publications

Exchange of Geometric Information Between Applications

Exchange of Geometric Information Between Applications

An algebraic taxonomy for locus computation in dynamic geometry

Automatic deduction in (dynamic) geometry: Loci computation

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