Deciding geometric properties symbolically in GeoGebra

It is well known that Dynamic Geometry (DGS) software systems can be useful tools in the teaching/learning of reasoning and proof. GeoGebra 5.0 was recently extended by an Automated Theorem Prover (ATP) subsystem that is able to compute proofs of Euclidean geometry statements. Free availability and portability of GeoGebra has made it possible to harness these novel techniques on tablets, smartphones and computers. Then, we think it is urgently necessary to address the new challenges posed by the availability of geometric ATP?s to millions of students worldwide

Conjuntos preanalíticos, prenashicos y prealgebraicos

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, leída el 11/11/1976Fac. de Ciencias MatemáticasTRUEunpu

On the Unavoidable Uncertainty of Truth in Dynamic Geometry Proving

The aim of this note is to discuss some issues posed by the emergency of universal interfaces able to decide on the truth of geometric statements. More specifically, we consider a recent GeoGebra module allowing general users to verify standard geometric theorems. Working with this module in the context of Varignon’s theorem, we were driven – by the characteristics of the GeoGebra interface– to perform a quite detailed study of the very diverse fate of attempting to automatically prove this statement, when using two different construction procedures.We highlight the relevance –for the theorem proving output– of expression power of the dynamic geometry interface, and we show that the algorithm deciding about the truth of some –even quite simple– statements can fall into a not true and not false situation, providing a source of confusion for a standard user and an interesting benchmark for geometers interested in discovering new geometric facts

Computing envelopes in dynamic geometry environments

We review the behavior of standard dynamic geometry software when computing envelopes, relating these approaches with the various definitions of envelope. Special attention is given to the recently released version of GeoGebra 5.0, that implements a recent parametric polynomial solving algorithm, allowing sound computations of envelopes of families of plane curves. Specific details on this novel approach are provided in this paper

Using Maple's RegularChains library to automatically classify plane geometric loci

We report a preliminary discussion on the usability of the RegularChains library of Maple for the automatic computation of plane geometric loci and envelopes in graphical interactive environments. We describe a simple implementation of a recently proposed taxonomy of algebraic loci, and its extension to envelopes of families of curves is also discussed. Furthermore, we sketch how currently unsolvable problems in interactive environments can be approached by using the RegularChains library

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)

Seminario "Itinerario Educativo de la Licenciatura de Matemáticas" Documento de conclusiones y respuestas

La Subcomisión Española de la International Comission on Mathematics Education1 ha celebrado un Seminario2 dedicado al análisis y diseño de líneas maestras para un “Itinerario Educativo de la Licenciatura de Matemáticas. Conclusiones y sugerencias recogidas durante el Seminario, presentadas y debatidas colectivamente en su última jornada, a fin de posibilitarComisión Española de Matemáticas CEMa

A propósito de la envolvente de una familia de elipses

En esta nota se estudia la envolvente de una familia de curvas constituida por las elipses con un foco fijo en el punto A(4, 0), otro foco variable B(0, _) y longitud de eje mayor igual a 5. El cálculo de esta envolvente sirve como motivación para reflexionar sobre diversas dificultades ligadas a la incorporación del cálculo automático de envolventes en programas de geometría dinámica, como parte del objetivo, más general, de dotar a tales programas de capacidades de razonamiento geométrico (demostración, derivación, descubrimiento, cálculo de lugares, etc.) automático

Enunciados ni ciertos ni falsos en razonamiento automático en geometría

ABSTRACT: We investigate and generalize to an extended framework the notion of true on components labeled by Zhou, Wang and Sun in their paper "Automated Reducible Geometric Theorem Proving and Discovery by Gröbner Basis Method", J. Automat. Reasoning 59 (3), 331-344, 2017. A new, simple criterion is presented for a statement to be simultaneously not generally true and not generally false (i.e. true on components), and its performance is exemplified through the implementation of this test in the dynamic geometry program GeoGebra. This extended abstract is based on a recent work by the authors.Partially supported by the Spanish Research Project MTM2017-88796-P Computación simbólica: nuevos retos en álgebra y geometría y sus aplicaciones