  We solve the long-standing problem of making n perfect clones from m copies
of one of two known pure states with minimum failure probability in the general
case where the known states have arbitrary a priori probabilities. The solution
emerges from a geometric formulation of the problem. This formulation also
reveals a deeper connection between cloning and state discrimination. The
convergence of cloning to state discrimination as the number of clones goes to
infinity exhibits a phenomenon analogous to a second order symmetry breaking
phase transition.
