Leonardo da Vinci's Vitruvian Man (c. 1490) represents one of the most analyzed yet cryptic works in art history. While the drawing's symbolic significance as representing ideal human proportions has been extensively documented, the precise geometric system Leonardo used to establish the relationship between the circumscribing circle and square has remained mysteriously elusive for over five centuries.
The challenge originates from Vitruvius himself, who proposed in ‘De Architectura’ that the perfectly proportioned human figure could be inscribed within both a circle and a square, but provided no mathematical framework for achieving this geometric relationship. As Murtinho (Citation2015) documents, ‘nowhere in the Vitruvian treaty is there a clarification of the proportional system that establishes the relational factor between the square and the circle. This situation has led to immense geometric and symbolic speculation in terms of the search for and definition of the rules that will have guided Leonardo to the drawing of his Vitruvian man.’
This geometric question has attracted scholarly investigation for centuries because Leonardo achieved what Vitruvius only proposed – a precise mathematical relationship that successfully inscribes the human figure within both geometric forms. Understanding Leonardo's construction method has implications beyond art history, potentially revealing sophisticated mathematical and anatomical insights embedded within Renaissance artistic practice.