A Vitruvius Inspired Criterion for the Construction of Polygons

Abstract

A geometric analysis carried out on three homonymous works, known as the Vitruvian man, by Leonardo da Vinci, Giacomo Andrea da Ferrara and Gulielmo Philandro has identified the equilateral triangle as a common feature, differing only with respect to the central position of the apex. Considerations regarding the intended purpose of the tangential outer arc in the Ferrara’s sketch and the possible implications of the two secants, drawn from the mid-point at the base to its intersections with the sides of the square, have provided the basis for a general construction of polygons. The underlying criterion relies on the parameters that define the geometric components of the arc to establish the position of the vertices of the polygon. The fundamental nature of the construction was confirmed through a comparison with an existing procedure by Fletcher, named “squaring the circle”.