Un método pararnétrico para demostrar automáticamente y determinar lugares a partir de las construcciones geométricas

Resumen

Both Computer Algebra Systems (CASs) and Dynamic Geometry Systems (DGSs) have reached a high level of development, but they have evolved separately: CASs have incorporated neither mouse drawing nor dynamic capabilities, meanwhile DGSs do not provide algebraic facilities. Our aim is to convert the geometric configuration drawn using the mouse with the DGS into CAS-acceptable sintaxis, because CASs can compute equations exactly and can also perform symbolic manipulations (e.g. of equations of geometric objects). After analyzing theoretically the situation, a constructive approach that considers parameters as the coordinates of free points and carries them along all subsequent calculations, has been developed. A corresponding Euclidean Geometry package, denoted paramGeo, has been developed and implemented for two existing CASs, together with an external translator (that converts the geometric algorithm created with the DGS, into any of those two CASs' syntax). To perform automatic theorem proving and to determine automatically geometric loci, starting from geometric configurations, are direct applications. Finally, a comparison with classic methods based in Synthetic Geometry is included.