Catálogo de publicaciones - libros

A package for investigating problems about configuration theorems in 3D-geometry and performing mechanical theorem proving and discovery is presented. It includes the preparation of the problem, consisting of three processes: defining the geometric objects in the configuration; determining the hypothesis conditions through a point-on-object declaration method; and fixing the thesis conditions. After this preparation, methods based both on Groebner Bases and Wu’s method can be applied to prove thesis conditions or to complete hypothesis conditions. Homogeneous coordinates are used in order to treat projective problems (although affine and Euclidean problems can also be treated). A Maple implementation of the method has been developed. It has been used to extend to 3D some classic 2D theorems.

Real Euclidean geometry is a basic mathematical dialect, not only of high school students, but also of mechanical engineers, graphics programmers, architects, surveyors, machinists, and many more. In this paper, we present ”Geometry Expressions”: an interactive symbolic geometry package. The aim of the software is to generate algebraic formulas from geometry. It is a further intention of the software that the model should be entered interactively in a style which is convenient to both the geometry consumer groups identified above.

Employing a method of distance geometry, we present a symbolic solution to the following problem: express the edge-lengths of a tetrahedron in terms of its heights and widths.