410 research outputs found
Using Automated Reasoning Tools in GeoGebra in the Teaching and Learning of Proving in Geometry
ABSTRACT: This document introduces, describes and exemplifies the technical features of some recently implemented automated reasoning tools in the dynamic mathematics software GeoGebra. The new tools are based on symbolic computation algorithms, allowing the automatic and rigorous proving and discovery of theorems on constructed geometric figures. Some examples of the use in the classroom of such commands are provided, including one describing how intuitive handling of GeoGebra automated reasoning tools may result in unexpected outputs. In all cases the emphasis is made in the potential utility of these tools as a guiding stick to foster student activities (exploration, reasoning) in the learning of elementary geometry. Moreover, a collection of appendices describing other, more sophisticated, low-level GeoGebra tools (Prove, ProveDetails), as well as instructions on how to obtain the translation of GeoGebra commands into other languages, and details about debugging, are included.Work partially supported by the grant MTM2017-88796-P from the Spanish MINECO and the ERDF (European
Regional Development Fund)
Automatic Deduction in Dynamic Geometry using Sage
We present a symbolic tool that provides robust algebraic methods to handle
automatic deduction tasks for a dynamic geometry construction. The main
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. In one worksheet, diagrams constructed with the open
source dynamic geometry system GeoGebra are accepted. In this worksheet,
Groebner bases are used to either compute the equation of a geometric locus in
the case of a locus construction or to determine the truth of a general
geometric statement included in the GeoGebra construction as a boolean
variable. In the second worksheet, locus constructions coded using the common
file format for dynamic geometry developed by the Intergeo project are accepted
for computation. The prototype and several examples are provided for testing.
Moreover, a third Sage worksheet is presented in which a novel algorithm to
eliminate extraneous parts in symbolically computed loci has been implemented.
The algorithm, based on a recent work on the Groebner cover of parametric
systems, identifies degenerate components and extraneous adherence points in
loci, both natural byproducts of general polynomial algebraic methods. Detailed
examples are discussed.Comment: In Proceedings THedu'11, arXiv:1202.453
Integrating DGSs and GATPs in an Adaptative and Collaborative Blended-Learning Web-Environment
The area of geometry with its very strong and appealing visual contents and
its also strong and appealing connection between the visual content and its
formal specification, is an area where computational tools can enhance, in a
significant way, the learning environments.
The dynamic geometry software systems (DGSs) can be used to explore the
visual contents of geometry. This already mature tools allows an easy
construction of geometric figures build from free objects and elementary
constructions. The geometric automated theorem provers (GATPs) allows formal
deductive reasoning about geometric constructions, extending the reasoning via
concrete instances in a given model to formal deductive reasoning in a
geometric theory.
An adaptative and collaborative blended-learning environment where the DGS
and GATP features could be fully explored would be, in our opinion a very rich
and challenging learning environment for teachers and students.
In this text we will describe the Web Geometry Laboratory a Web environment
incorporating a DGS and a repository of geometric problems, that can be used in
a synchronous and asynchronous fashion and with some adaptative and
collaborative features.
As future work we want to enhance the adaptative and collaborative aspects of
the environment and also to incorporate a GATP, constructing a dynamic and
individualised learning environment for geometry.Comment: In Proceedings THedu'11, arXiv:1202.453
Automated Theorem Proving in GeoGebra: Current Achievements
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
Towards a Geometry Automated Provers Competition
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 discovery at EGMO 2022
Este estudo mostrará a capacidade (ou incapacidade) da GeoGebra Discovery de lidar com problemas de geometria euclidiana propostos na recente OlimpĂada Europeia de Matemática das Meninas (Hungria, 6 a 12 de abril de 2022). ApĂłs uma breve introdução ao contexto desta OlimpĂada e ao programa GeoGebra Discovery, os problemas serĂŁo descritos e será feita uma tentativa de resolvĂŞ-los com a GeoGebra Discovery, finalmente apontando a relação entre as dificuldades encontradas pelos membros da equipe e pela GeoGebra, que podem contribuir para o estabelecimento de critĂ©rios sobre o interesse (e complexidade) dos resultados obtidos automaticamente
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