Abstract
The use of 3D dynamic geometry systems (D3DGS) opens new topics in spatial geometry. These systems provide opportunities for discovery learning (enrichment) and support the application of heuristic methods for theorem finding (reinforcement). One of these topics is billiards in convex polyhedra. Discovering distinctive billiards trajectories in a cube and its generalizations is suitable for spatial geometry activities beyond regular classroom lessons. It is equivalent to the discovery of inscribed polygons with minimal perimeter. The findings reveal that spatial polygons may be similarly used to mark special convex polyhedra.
Billiards in Euclidean spaces of dimension three or more are essentially in an infantile state. In brief: practically nothing is known in general.
−Berger (2010)
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Schumann, H. (2019). Using 3D Geometry Systems to Find Theorems of Billiard Trajectories in Polyhedra. In: Hanna, G., Reid, D., de Villiers, M. (eds) Proof Technology in Mathematics Research and Teaching . Mathematics Education in the Digital Era, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-030-28483-1_12
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