Search

Dynamic Geometry Systems (DGS) are the Graphic User Interfaces for Automatic Deduction in Geometry (ADG). We will develop below some reflections regarding how geometric data are introduced to the most frequently adopted DGS and how the constructive geometric processes (that are similar to the programs of "usual" computer languages) are stored. The later can be used as input for ADG processes.

A method that automates hypotheses completion in 3D-Geometry is presented. It consists of three processes: defi ning the geometric objects in the confi guration; determining the hypothesis conditions of the confi guration (through a point-on-object declaration method); and applying an algebraic automatic theorem proving method to obtain and prove the sufficiency of complementary hypothesis conditions. To avoid as much as possible the appearance of rational expressions, projective coordinates are used (although affine and Euclidean problems can also be treated). A Maple implementation of the method has been used to extend to 3D classic 2D geometric theorems like Ceva's and Menelaus'.