Dedekind sums and class numbers

Formulas for the class number of an imaginary quadratic number field are proved. Some of these formulas were previously established by Berndt and by Goldstein and Razar with the use of analytic methods. The proofs given here use Dirichlet's classical class number formula, but otherwise the proofs are completely elementary. A key ingredient in the proofs is the reciprocity theorem for Dedekind-Rademacher sums.