Jesús Escribano

Exact internet accessible computation of paths of points in planar linkages and diagrams

Dynamic Geometry, also known as Interactive Geometry, refers to computer programs where accurate construction of (generally) planar drawings can be made. The key characteristic of this software is that, when dragging certain elements of the configuration, the geometric properties of the construction are preserved. In this paper, we describe an educational web‐based application that complements standard dynamic geometry programs in a mathematically sound manner. We put the focus on computing the geometric locus of distinguished points in linkages and other geometric constrained configurations, since knowing the equations of such loci is a typical engineering task. The tool is located at http://nash.sip.ucm.es/LAD/LADucation.html.

Adding remote computational capabilities to Dynamic Geometry Systems

A Dynamic Geometry System (DGS) is a computer application that allows the exact drawing and dynamic manipulation of geometric constructions. DGS have been the paradigm of new technologies applied to Math education, but some authors have claimed that some symbolic capabilities should be added to this systems. We present an example of communication between the commercial DGS Cabri, The Geometers Sketchpad and Cinderella and two Computer Algebra Systems (CAS), Mathematica and CoCoA. The tool is a web application designed to symbolically process locus, proof and discovery tasks on geometric diagrams. Named LAD (Locus-Assertion-Discovery), it is a remote add-on for the three DGS. LAD is a prototype oriented to research users. We also describe LADucation, a one-click educational version of LAD. By just uploading the file generated by the considered DGS, graphs and equations of geometric loci are computed.

Using a free open source software to teach mathematics

We present the experience of the authors teaching mathematics to freshmen engineering students with the help of the open source computer algebra system Sage. We describe some teaching resources and present an ad hoc distribution of Sage used by the authors.© 2012 Wiley Periodicals, Inc. Comput Appl Eng Educ 22:728–735, 2014; View this article online at wileyonlinelibrary.com/journal/cae; DOI 10.1002/cae.21565

Computing Locus Equations for Standard Dynamic Geometry Environments

GLI (Geometric Locus Identifier), an open web-based tool to determine equations of geometric loci specified using Cabri Geometryand The Geometers Sketchpad, is described. A geometric construction of a locus is uploaded to a Java Servlet server, where two computer algebra systems, CoCoA and Mathematica, following the Groebner basis method, compute the locus equation and its graph. Moreover, an OpenMath description of the geometric construction is given. GLI can be efficiently used in mathematics education, as a supplement of the locus functions of the standard dynamic geometry systems. The system is located at http://nash.sip.ucm.es/GLI/GLI.html .

First Steps on Using OpenMath to Add Proving Capabilities to Standard Dynamic Geometry Systems

A prototype for a web application designed to symbolically process locus, proof and discovery tasks on geometric diagrams created with the commercial dynamic geometry systems Cabri, The Geometers Sketchpadand Cinderellais presented. The application, named LAD (acronym for Locus-Assertion-Discovery) and thought of as a remote add-onfor the considered DGS, follows the Groebner basis method relying on CoCoA and a Mathematica kernel for the involved symbolic computations. From the DGS internal textual representation of a geometric diagram, an OpenMath (i.e. semantic based) description of the requested task is created using the elements in the plangeoOpenMath content dictionaries. A review of the elements included in these CDs is given and two new elements proposed, namely locusand discovery. Everything is finally thoroughly illustrated with examples. LAD is freely accessible at http://nash.sip.ucm.es/LAD/LAD.html .

Automated Generation of Equations for Linkage Loci in a Game Physics System

There is no doubt about the prevalence of dynamic geometry (DG) as the preferred technological tool among math teachers. DG systems are tools for geometric visualization that allow users to construct geometric elements and establish relationships among them. The key property of DG is that the system automatically updates the whole geometric diagram, preserving its constraints when one element is dragged with the mouse. Its known limitations concerning symbolic computations are being progressively overcome as DG programs walk towards a more friendly integration with computer algebraic systems. It is reasonable to think that it is just a question of time that an

Using free open source software for intelligent geometric computing

This paper describes some examples of fruitful cooperation between geometric software tools (in particular, GeoGebra) and a free open source computer algebra system, Sage (Software for Algebra and Geometry Experimentation). We collect some of our efforts for enhancing mathematics education via technologically rich environments. We show that a math teacher with no specialized programming knowledge can mix widespread resources to get motivating new teaching tools. Furthermore, we explore an exciting but barely used (even known!) characteristic of Sage: its use as a remote kernel. We test it by computing symbolic tasks in a dynamic geometry prototype that are currently out of scope of standard dynamic geometry software. Finally, we illustrate the development of web-based geometric resources by communicating GeoGebra and Sage through Javascript.

Bifurcation sets of definable functions in o-minimal structures

In this work we answer a question stated by Loi and Zaharia concerning trivialization of definable functions off the bifurcation set: we prove that definable functions are trivial off the bifurcation set, and the trivialization can be chosen definable.