9 research outputs found

    Towards a Geometry Automated Provers Competition

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    The geometry automated theorem proving area distinguishes itself by a large number of specific methods and implementations, different approaches (synthetic, algebraic, semi-synthetic) and different goals and applications (from research in the area of artificial intelligence to applications in education). Apart from the usual measures of efficiency (e.g. CPU time), the possibility of visual and/or readable proofs is also an expected output against which the geometry automated theorem provers (GATP) should be measured. The implementation of a competition between GATP would allow to create a test bench for GATP developers to improve the existing ones and to propose new ones. It would also allow to establish a ranking for GATP that could be used by "clients" (e.g. developers of educational e-learning systems) to choose the best implementation for a given intended use.Comment: In Proceedings ThEdu'19, arXiv:2002.1189

    GeoGebra as a learning mathematical environment

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    GeoGebra, a software system for dynamic geometry and algebra in the plane, since its inception in 2001, has gone from a dynamic geometry software (DGS), to a powerful computational tool in several areas of mathematics. Powerful algebraic capabilities have joined GeoGebra, an efficient spreadsheet that can deal with many kinds of objects, an algebraic and symbolic calculation system and several graphical views that expand the possibility of multidimensional representations, namely, by using colouring domain techniques, expanded to representations in the Riemann sphere, making this DGS a powerful research tool in mathematics. On the other hand, GeoGebra can create applications easily and export to HTML, and the possibility to quickly integrating these applets in several web platforms provides this DGS with an excellent way to create strong collaborative environments to teach and learn mathematics. Recently was added to GeoGebra powerful capabilities that transform this software a real Learning Mathematical Environment, using the GeoGebraBooks and GeoGebraGroups, plain of collaborative functionality between students and teachers

    Automated Theorem Proving in GeoGebra: Current Achievements

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    GeoGebra is an open-source educational mathematics software tool, with millions of users worldwide. It has a number of features (integration of computer algebra, dynamic geometry, spreadsheet, etc.), primarily focused on facilitating student experiments, and not on formal reasoning. Since including automated deduction tools in GeoGebra could bring a whole new range of teaching and learning scenarios, and since automated theorem proving and discovery in geometry has reached a rather mature stage, we embarked on a project of incorporating and testing a number of different automated provers for geometry in GeoGebra. In this paper, we present the current achievements and status of this project, and discuss various relevant challenges that this project raises in the educational, mathematical and software contexts. We will describe, first, the recent and forthcoming changes demanded by our project, regarding the implementation and the user interface of GeoGebra. Then we present our vision of the educational scenarios that could be supported by automated reasoning features, and how teachers and students could benefit from the present work. In fact, current performance of GeoGebra, extended with automated deduction tools, is already very promising—many complex theorems can be proved in less than 1 second. Thus, we believe that many new and exciting ways of using GeoGebra in the classroom are on their way

    O método do ângulo completo

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    Dissertação de Mestrado em Matemática, área de Especialização em Análise Aplicada e Computação, apresentada à Faculdade de Ciências e Tecnologia da Universidade de CoimbraEste trabalho descreve o Método do Ângulo Completo para a geometria euclidiana construtiva assim como a sua implementacão no âmbito do Open Geo Prover. O Método do Ângulo Completo é baseado na noção de ângulo completo e num conjunto de axiomas e regras de inferência. Apresentamos um conjunto de regras de inferência para o método do ângulo completo como sendo a base de demonstrações automatizadas de teoremas de geometria. Este método é uma extensão do método da área, obtendo-se a partir deste pela introdução de uma nova quantidade geométrica designada por ângulo completo. Descreve-se também a implementação do método do ângulo completo no projecto Open Geo Prover.This paper describes the Full Angle Method for constructive Euclidean geometry and its implementation on the Open Geo Prover project. The Full Angle Method is based on the notion of full angle and a set of axioms and inference rules. We present a set of rules based on the full angle as being a basis to automatic demonstration of geometry theorems. This method is an extension of the area method that we can obtain by introducing a new geometric quantity, designated the Full Angle. We also describe the implementation of the full angle method on the Open Geo Prover project

    O método do ângulo completo no sistema OpenGeoProver

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    Dissertação de Mestrado em Matemática apresentada à Faculdade de Ciências e Tecnologia da Universidade de CoimbraO método do ângulo completo para geometria euclideana construtiva foi proposto por Chou, Gao e Zhang no início dos anos 1990. Este método, uma extensão do método da área proposto pelos mesmos autores, produz demonstrações legíveis e de um modo eficiente demonstra muitos teoremas não triviais. Pode ser considerado como um dos métodos mais interessante e de maior sucesso na demonstração de teoremas em geometria e, possivelmente, o mais bem sucedido na produção de demonstrações automáticas legíveis. Nesta dissertação de mestrado faz-se a apresentação do mêtodo do ângulo completo e demonstram-se muitos dos seus lemas. Descreve-se ainda a planificação da implementação, em código livre, do método do ângulo completo.The full-angle method for euclidean constructive geometry was proposed by Chou, Gao, Zhang in early 1990’s. The method, an extension of the area method proposed by the same authors, produces humanreadable proofs and can efficiently prove many non-trivial theorems. It can be considered as one of the most interesting and most successful methods in geometry theorem proving and probably the most successful in the domain of automated production of readable proofs. In this master thesis a presentation of the full-angle method is made and several of its lemmas are proved. A plannification of the implementation, in open source code, of the full-angle method is also described
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