The minima of indefinite binary quadratic forms

The study of the minima of indefinite binary quadratic forms has a long history and the classical results concerning the determination of such minima are stated in terms of the continued fraction expansion of the roots. These results are recast in geometric terms. Using this, and well-known geometric properties of the modular group, some necessary and sufficient conditions for a certain class of quadratic forms to have positive unattained minima are obtained.