  We show explicitly that all 2nd order superintegrable systems in 2 dimensions
are limiting cases of a single system: the generic 3-parameter potential on the
2-sphere, S9 in our listing. We extend the Wigner-In\"on\"u method of Lie
algebra contractions to contractions of quadratic algebras and show that all of
the quadratic symmetry algebras of these systems are contractions of that of
S9. Amazingly, all of the relevant contractions of these superintegrable
systems on flat space and the sphere are uniquely induced by the well known Lie
algebra contractions of e(2) and so(3). By contracting function space
realizations of irreducible representations of the S9 algebra (which give the
structure equations for Racah/Wilson polynomials) to the other superintegrable
systems, and using Wigner's idea of "saving" a representation, we obtain the
full Askey scheme of hypergeometric orthogonal polynomials. This relationship
directly ties the polynomials and their structure equations to physical
phenomena. It is more general because it applies to all special functions that
arise from these systems via separation of variables, not just those of
hypergeometric type, and it extends to higher dimensions.
