Approximations between Algebra and Geometry: use of the concept of arithmetic progression in the division of segments of straight lines in equidistant points

Abstract

The learning of concepts in mathematics implies the perception of relationships between different approaches, be they through arithmetic, algebra or geometry. In this paper, an alternative proposal for the resolution of a classic problem of analytic geometry is presented, which deals with the division of a segment into a given ratio, that was perceived by an undergraduate student in mathematics during a course called “Analytical Geometry”. The bibliographic research indicated that there are different modes of resolution, but a method similar to that proposed by the student was not found. It was concluded that this perception, which implies in the use of both geometric and algebraic concepts, can favor the teaching and meaningful learning of mathematics, since it allows to stimulate the use of already existing concepts, such as the concepts of midpoint, points equidistant and arithmetic progression, as well as stimulates the development of competence in transit between different semiotic registers.