The Regular Polyhedra: Drawing and Computing in Euclid’s day

Abstract

Can we compute what we cannot draw? How must we draw to produce measurable representations, or visual ones? This research inquires into the relationship between mathematics and figurative representation, and more precisely between drawing and computation. The scientific imagery studied here is the representation of the five platonic solids, discussing various representation techniques from classical antiquity to modern times, and their efficacy to help calculate sizes and proportional ratios. Scholars in history of architectural drawing have too often limited their observations to the very few preserved plans and front views dating back to classical antiquity, without enlarging their investigation to other scientific fields that also rely on drawing as a research tool and communication device. Among these other fields stands the mathematical research, especially solid geometry which deals with objects and entities that have shapes that needs to be somehow drawn in 3D to be studied.