I will soon be teaching an introductory course on bilinear algebra and quadratic forms. I will likely spend most of the time and effort on positive definite quadratic forms and euclidean spaces. These have nice and concrete (i.e. not to theoretical physics) applications since they are basic for many optimisation problems. Are there any applications of this type (so not Einstein's relativity theory) which involve isotropic forms (and which hopefully would be useful beyond just motivating the material for bored undergraduates, e.g. that would be a basis for a problem or a series of exercises)?