Laboratorio di geometria ricorrente sul cerchio dei nove punti

Abstract

Recurrent geometry, devised by the French mathematician Gaston de Longchamps (1842-1906), who, in his 1883 article La Géométrie Récurrente, based on certain remarkable points of the triangle, such as the circumcentre, the orthocentre and the barycentre, and on objects related to the geometry of the triangle, such as the nine-point circle and the Simson-Wallace line, created chains of theorems that depend on each other in an iterative manner. The interest in such topics stems from the fact that at school, the recursive process is only developed in the arithmetic domain, and not in the geometric one. Following up on the Recurrent Geometry Workshop on the Circumcentre carried out in a scientific high school during the school year 2022/23, the aim of this paper is to present a workshop focusing on de Longchamps' chain related to the nine-point circle associated with a triangle.