Un Acercamiento A La Relación Pitagórica A Través Del Cálculo De Ternas

Abstract

The Pythagorean Theorem and more formally the Pythagorean Relationship (PR), is one of the most well-known and used results in the context of school mathematics, given that it is an axis of conceptual articulation between different areas of Mathematics. However, in the school context it is common for a Didactic Reductionism to be presented, only enunciating it and presenting the algebraic expression that relates the squares of the sides of a right triangle, leaving aside its great historical and epistemological significance. In view of this problem, this documentary research aims to design an alternative proposal to broaden the understanding of the Pythagorean Relationship, which is based on the calculation of Pythagorean Ternas. Three different methods are proposed to generate positive integers, that satisfy the Pythagorean Theorem and suggest questions that can guide learning activities to promote the understanding of some important elements within Mathematics, particularly in reference to the identification of numerical patterns.