More than 500 Greco-Roman sundials are extant in varying degrees of preservation (Bonnin 2012). There is a profusion of types, differentiated by shape and orientation, for example spherical and conical bowls, horizontal planes, equatorial planes, and vertical planes facing the various cardinal directions (Gibbs 1976). While the most common manner in which the moving Sun indicates the time of day and year is by a gnomon shadow, some types project sunlight through an eyehole on a shaded surface, or track the moving boundary between the illuminated and shaded part of the sundial's surface. Practical constraints such as the layout of the buildings and sites where sundials were to be mounted provide a partial but insufficient explanation of the variety of sundial types.
Vitruvius, De Architectura 9.8 lists thirteen types of sundial according to Greek and Latin names that are notoriously difficult to match with types known from surviving examples. What is most significant about this passage is the high proportion of prominent mathematicians among the figures to whom Vitruvius attributes the invention of various sundials. Whether or not the attributions are historically correct, they reflect an ancient view that the sundial was not merely a practical device and a product of craft but also a physical instantiation of mathematics and mathematical astronomy.
The present paper will illustrate several ways in which sundials provided a public face for mathematical virtuosity. Planar sundials, including the eight exterior walls of the Tower of the Winds in Athens, embodied what was ostensibly the most advanced and abstract topic in Greek geometry, the study of conic sections. So-called roofed spherical sundials, among which an ornamentally elegant and accurate example was recently acquired by the Louvre (Ma 5074, Savoie & Lehoucq 2001), exploited Hellenistic techniques of transforming special curves through projections. Lastly, we will consider two remarkable globe-shaped sundials found at Macerata (Marche) and Prosymna (Argolid), which combine mathematical sophistication with a cosmological lesson in that the sundial becomes an image of the terrestrial globe (Schaldach & Feustel 2013).
Representation of Time in the Hellenistic and Roman World