The starting point of this research is Fagnano’s problem: “For a given acute triangle, determine the inscribed triangle of the minimal perimeter.” This problem has been investigated using methodologies both from mathematical analysis and synthetic geometry, and many demonstrative strategies have been provided. The orthic triangle is the problem's solution. This problem has been recently extended to convex quadrilaterals. In particular, Fagnano's problem is relevant in billiard physics: the orthic triangle is the minimum periodic orbit of an acute triangular billiard. An open question still remains referring to quadrilaterals: "Are the Orthic Quadrilaterals the minimum periodic orbits in a real billiard?" This communication aims to describe experimental teaching in an Italian high school, focused on Mathematical and Physical tasks, from a historical perspective. Starting from a historical and epistemological context, an interdisciplinary learning path has been planned, which has been experimented with about sixty fifteen-year-old students. The applicability of some geometric theorems to different contexts of reality has been tested through the realization and use of specific artifacts as teaching materials.
THE HISTORICAL FAGNANO'S PROBLEM: TEACHING MATERIALS AS ARTIFACTS TO EXPERIMENT MATHEMATICAL AND PHYSICAL TASKS IN ITALIAN HIGH SCHOOL
Roberto Capone;
2023-01-01
Abstract
The starting point of this research is Fagnano’s problem: “For a given acute triangle, determine the inscribed triangle of the minimal perimeter.” This problem has been investigated using methodologies both from mathematical analysis and synthetic geometry, and many demonstrative strategies have been provided. The orthic triangle is the problem's solution. This problem has been recently extended to convex quadrilaterals. In particular, Fagnano's problem is relevant in billiard physics: the orthic triangle is the minimum periodic orbit of an acute triangular billiard. An open question still remains referring to quadrilaterals: "Are the Orthic Quadrilaterals the minimum periodic orbits in a real billiard?" This communication aims to describe experimental teaching in an Italian high school, focused on Mathematical and Physical tasks, from a historical perspective. Starting from a historical and epistemological context, an interdisciplinary learning path has been planned, which has been experimented with about sixty fifteen-year-old students. The applicability of some geometric theorems to different contexts of reality has been tested through the realization and use of specific artifacts as teaching materials.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
