Eugenio Roanes Macias & Eugenio Roanes Lozano

Automated Search for Geometric Loci

Looking for geometric loci is easier using suitable computer systems. A Dynamic
Geometry System can help in a first exploration of the problem and a Computer
Algebra System is necessary to use algebraic methods of mechanical proving. How
to use the last one in the discovering process and how to proof theorems
relative to geometric loci in a automatic way is described. Two examples are
shown as illustration: the extension of Simson's theorem (discovered last
century by Jakob Steiner) and a second extension (recently found by Professor
Miguel de Guzman).