Circular Tessellations

Abstract

Some particularly beautiful examples of logarithmic spirals turn up if we cover the plane with equally shaped geometric elements such that the number of elements along concentric circles is constant. An excellent illustration is the astonishing floor mosaic from a second century AD Roman villa in Corinth, Greece, showing Dionysos (some say Apollo) in the center surrounded by a circular tessellation of triangles (Fig. 11.1). The dizzying display with the god of wine in the middle must have been quite a party piece! The question is what the local Greek mathematician would have said if invited to dinner, for the geometry here is worth a closer study.