Dos triângulos de Brahmagupta aos triângulos aritméticos

Abstract

This work, the result of bibliographic research, presents a study on heronian triangles with sides in arithmetic progression and properties that relate them to Pythagorean triangles, in addition to showing a practical and easy way to obtain them by parameterizing their sides. It deals specifically with the heronian triangles with consecutive sides in honor of the Indian mathematician, Brahmagupta, on the merit of having presented the first eight triangles with such property, hereinafter called the Brahmagupta Triangles. The work exhibits the ingenious method, the Samasa Bhãvanã, or principle of composition, for calculating the infinite integer solutions of the Diophantine equations today known as “Pell's equations”, a method developed by Brahmagupta in the seventh century of the Christian era, which probably must have been the means whereby that mathematician used to obtain the first eight heronian triangles with consecutive sides. It is also the purpose of this work to show the involvement between algebra, number theory and geometry, throughout the millenary history of mathematics. This work is aimed at basic education students and teachers who want to deepen their studies on the heronian triangles.