ABSTRACT. The purpose of the paper is threefold:

(1) To develop a useful error bound for the method of alternating projections which is relatively easy to compute and remember;

(2) To exhibit a counterexample to a conjecture of Kayalar and Weinert;

(3) To show that (in the case of at least three subspaces) any error bound which only depends on the angles between the various subspaces involved can never be sharp.