The algebraic theory of quadratic forms applied to a dispute between two orixás

Abstract

This is an brief and ludic introduction to the Algebraic Theory of Quadratic Forms, as presented in [1], and intermediated by fables or anecdotes from Brazilian Candomblé told in [2], in order to expose and strengthen the Theory of Quadratic Forms among the Brazilian community, because that this is a broad theory within Mathematics (for example, with connections in number theory and real algebraic geometry), and with important contributions made by Latin American mathematicians, such as the contributions of professors F. Miraglia and M. Dickmann in the articles [3] and [4], and the contribution of Professor M. Spira in the article [5]. The text focuses on presenting the initial concepts of the theory, such as quadratic form, quadratic spaces, elements represented by a form, discriminant, hyperbolicity, anisotropy and diagonalization of forms. After that, a fable is presented (inspired by the style of R. Smullyan in [6], and by the topological games) involving a dispute between Orixás solved through a game that uses elements of arithmetic in quadratic forms, as a ludic way of involving /interest the reader in the beautiful theory of quadratic forms through elements of Afro-Brazilian culture.