Print version ISSN 1665-5826
The present paper discusses two problems of geometric variation of remarkable historical importance: Fagnano's Problem, that relates to the perimeter of a triangle inscribed in a given acute triangle; and the Fermat's point Problem, that's relates the sum of distances from inner point to three vertex of a given acute triangle. Both problems involve fundamentals notions of the school curriculum and a variation process. Using a ruler or a dynamic software such as Cabri Geometry, you can see that if multiple reference points, the perimeter of the inscribed triangle and the sum of distances to the vertices change, the existence of minimum values for these variables corresponds to the solution of problems. Here we analyze the process of solution with different heuristic approaches and applications, highlighting the potential use of dynamic software and giving the geometric argument that justifies the solution.
Keywords : problem solving; variation; optimization; heuristic; symmetry.