Number theory | Quadratic forms
Bhargava cube
In mathematics, in number theory, a Bhargava cube (also called Bhargava's cube) is a configuration consisting of eight integers placed at the eight corners of a cube. This configuration was extensively used by Manjul Bhargava, a Canadian-American Fields Medal winning mathematician, to study the composition laws of binary quadratic forms and other such forms. To each pair of opposite faces of a Bhargava cube one can associate an integer binary quadratic form thus getting three binary quadratic forms corresponding to the three pairs of opposite faces of the Bhargava cube. These three quadratic forms all have the same discriminant and Manjul Bhargava proved that their composition in the sense of Gauss is the identity element in the associated group of equivalence classes of primitive binary quadratic forms. (This formulation of Gauss composition was likely first due to Dedekind.) Using this property as the starting point for a theory of composition of binary quadratic forms Manjul Bhargava went on to define fourteen different composition laws using a cube. (Wikipedia).
