Farey Colloquium

This is a talk given recently at colloquia at DePaul University and Montana State University.  I can’t find a good title for it, but it begins with the Farey fractions and the geometric viewpoint on continued fractions, then extends this to the complex plane.  The talk is full of pictures.  The picture at left is the Gaussian rationals, sized by norm of the denominator.  The picture at right is the Gaussian Schmidt arrangement.  In the talk, some of the pictures toward the end are due to my graduate student, Daniel Martin.