Arts , Humanities & Social Science

Abstract

The school reality presents us with two negative things, for the vast majority of students, in each class: on the one hand, Mathematics is a dry school subject, difficult to penetrate and, on the other hand, they learn Mathematics, thanks to one or more external motivations. In other words, Mathematics is a hard subject that is learned by force, not for pleasure. On the other hand, it is known that in order to learn Mathematics successfully, you must have a certain level of development of logical-mathematical thinking, but also a level of creative ability. Of course, these two levels increase as you learn Mathematics. In other words, the formation and development of logical-mathematical thinking and the ability to create is the cause and effect of learning Mathematics. Therefore, the Mathematics teacher must always have in mind, for each student, the raising of these two levels. In this paper we will present a concrete way to achieve this fact, "playing" with three equilateral triangles, in the idea of training and developing the competences to solve such problems. Thus, we will consider three equilateral triangles of different sides, each of which has one side located on a straight line d and the other sides located on the same side of this straight line. Moreover, the sides of these triangles which lie on the same straight line are in extension. We will determine, in this paper, a series of metric relations between the sides of these triangles, so that the angle formed by the three vertices not located on the right d is of an arbitrary measure. At the end of the paper, I proposed to the reader attentive and interested in these issues, the solution of four complementary problems to those solved in the paper.