Ternas pitagóricas suas relações e aplicações na Álgebra e na Geometria

This present article aims to show a new way to calculate the infinite Pythagorean cracks related as an equilateral hyperbola, through a direct proof. In addition to providing applications in plane and spatial geometry, showing the agility of knowledge and usefulness of the Pythagorean suits, making the relation of proportion with the sides of the right triangle, presenting two types of most common suits in geometric calculus, bringing with these cases, four usual and important types in geometry, the triangle of sides: 3,4 and 5; 5.12 and 13; 8, 15 and 17 and 7,24 and 25. The methodology is a diagnostic investigation and approach (quantitative), the study involved a quantitative approach that uses quantitative methods. This article offers two important cases of obtaining infinite tenders, but these four cases summarize most of the applications, thus discriminating new didactic transpositions important for the teaching of mathematics in the general context, facilitating the understanding and reducing the complexity of calculations.