Francisco Botana

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We describe the capabilities of Lugares for obtaining the equations and graphs of plane loci. Lugares is a Windows program written in Prolog that offers a standard dynamic geometry environment and uses the symbolic capabilities of CoCoA, a computer algebra system specialized in Groebner basis computations, or Mathematica. The main novelty in Lugares(More)
Dynamic geometry programs provide environments where accurate construction of geometric configurations can be done. Nevertheless, intrinsic limitations in their standard development technology mostly produce objects that are equationally unknown and so can not be further used in constructions. In this paper, we pursue the development of a geometric system(More)
This paper describes Discover, a program for learning and teaching geometry with the help of a computer. The program is a dynamic geometry environment that can communicate with Mathematica, using its symbolic capabilities to perform geometric discovery or rediscovery. Discover is specially suited to be used as a learning tool for geometry from the ages of(More)
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(More)
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(More)
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(More)
CeO(2) nanotubes have been grown electrochemically using a porous alumina membrane as a template. The resulting material has been characterized by means of scanning electron microscopy (SEM), X-ray energy dispersive spectroscopy, high-angle annular dark-field scanning transmission electron microscopy tomography, high-resolution electron microscopy (HREM),(More)
Outsourcing algebraic computations in dynamic geometry tools is a possible strategy used when software distribution constraints apply. If the target user machine has hardware limitations, or if the computer algebra system cannot be easily (or legally) packaged inside the geometric software, this approach can solve current shortcomings in dynamic(More)
GeoGebra is an open source mathematics education software tool being used in thousands of schools worldwide. Since version 4.2 (December 2012) it supports symbolic computation of locus equations as a result of joint effort of mathematicians and programmers helping the GeoGebra developer team. The joint work, based on former researches, started in 2010 and(More)