  We give an ergodic theoretic proof of a theorem of Duke about
equidistribution of closed geodesics on the modular surface. The proof is
closely related to the work of Yu. Linnik and B. Skubenko, who in particular
proved this equidistribution under an additional congruence assumption on the
discriminant. We give a more conceptual treatment using entropy theory, and
show how to use positivity of the discriminant as a substitute for Linnik's
congruence condition.
