El Problema dels ponts de Köningsberg. Idees per a l'aula

Abstract

We take the problem of the Bridges of Koningsberg to present to students a contextual situation that allows us to work on different aspects, curricular or not, of mathematics. Also, following on directly from the historical problem, it can be seen how, from a quite simple situation,major mathematical results that allow us to introduce other aspectsmore easily can be deduced. The introduction, by Euler, of a notation system that makes it possible to simplify and solve the problem of the Bridges (startingwith an easier problem, opening up the possibility of new forms of representation...) facilitates understanding by students of the situation and gives them the opportunity to dare to solve other similar situations, achieving personal satisfaction. Furthermore, the introduction of matrix notation andmatrix operations, especially the product, gives an added difficulty for students. With this approach, we managed to increase their interest and thus improve the results. The use of graph theory involves no further complication; on the contrary, students see it as a practical way to represent real situations facilitating subsequent reading and interpretation. Therefore, although not part of the high school curriculum, it is a good tool to introduce.