Research Based on Cabri 3D Software: Polyhedra Features and Regular Billiard Trajectories

Abstract

The usage of dynamic spatial geometry systems (DSGS) opens new opportunities for teachers, schoolchildren and students in studying topics related to spatial geometric figures. The DSGS programs, are prototypes of Cabri 3D, whose potential is fully used in studying the properties of polyhedra. One of these topics is the billiards in convex polyhedra. The study of special billiards in the cube and its generalizations are not included in the school program. The same can be said about inscribed spatial polygons of minimal perimeter that are used to define special convex hexahedra. Heuristic methods support experimental work with DSGS. Proofs of discovered assertions will be given in subsequent papers.