Abstract
Quaternions arise from the solution of an elementary two-dimensional polynomial, and can be visualized in terms of amplitude and phase spectra by means of a multidimensional Fourier transform. Three-dimensional quaternion configurations can be found in the structure of an octonion, including one that lies outside a plane, a tetrahedron. These configurations are formulated as polynomials and spectra of their quaternion and nonquaternion solutions are discussed in relation to the Higgs field.
Colin Walker