We prove existence and uniqueness results for patterns of circles with prescribed intersection angles on constant curvature surfaces. Our method is based on two new functionals--one for the Euclidean ...

Given a circle pattern on the Riemann sphere ℂ̂, in this paper we prove that its quasiconformal deformation space can be naturally identified with the product of the Teichmüller spaces of its ...

The artists behind increasingly elaborate crop-circle patterns are most likely skilled in math, necessary to plot epic designs, and technologically savvy enough to employ tools like microwave ...