The Geometry of Angels
We analyze the mathematical vision behind the wings of the angel Gabriel, in a Renaissaance painting, the Cortona Annunciation of Fra Angelico. In the context of the Renaisance mathematics of perspective and conic sections, the flapping wings generate a family of toroids. We interpret this image as a painterly representation of the three-sphere of Dante. As such, this geometrical vision of Fra Angelico presaged seminal works of modern mathematics, such as the Hopf fibration.