Visualizing Stokes' theorem with Geometric Algebra

Abstract

Foundational cases of the generalized Stokes' theorem are visualized using geometric algebra. From considering bivector valued fields, two seldom used instances of the theorem are obtained. Graphical representations are given, showing a radial spin structure corresponding to the generalized curl and a toroidal vortex for the generalized divergence. Dualities and applications to natural phenomena with non-trivial topology are discussed.