Paraphrased and extended from exercises 5.5--5.10 of Ian R. Porteous "Clifford Algebras and the Classical Groups" Cambridge (2000) --- surely familiar to those with a background in topology, but new to me. The circles and spheres are standard, rather than just homeomorphs. Given disjoint circles C,D in 3-space, consider the (Gauss) map from vectors joining pairs of points, X on C and Y on D, to the unit sphere: (X, Y) -> (X - Y)/|X - Y|. Show that this map is surjective if and only if the circles are linked; and specify its fibres (pre-images). Show that two disjoint great circles in spherical 3-space are always linked. Specify precisely a criterion to decide whether two circles in 3-space are (not) linked. Design a simple, effective algorithm to decide whether two circles in 3-space are linked. Show that two spheres may be linked in 5-space, but not in 4-space or 6-space. Generalise (inductively?) to decide whether k-sphere and l-sphere in (k+l+1)- space are linked. [The connection between such problems and the stated topic of section 5 --- the classification of real quadratic spaces --- itself constitutes an intriguing question, with regard to which I have yet to make progress.] Fred Lunnon