A London dentist has solved the geometric mystery of da Vinci's Vitruvian Man

The author of the discovery is not an art historian, but London dentist Rory Mac Sweeney, who published his findings in the Journal of Mathematics and the Arts.

Read more: Rory Mac Sweeney, Leonardo's Vitruvian Man: modern craniofacial anatomical analysis reveals a possible solution to the 500-year-old mystery, Journal of Mathematics and the Arts (2025). DOI: 10.1080/17513472.2025.2507568

For more than 500 years, scholars have tried to understand how da Vinci achieved the perfect alignment of the human figure with the circle and square - as suggested by the ancient Roman architect Vitruvius. However, Leonardo, having solved this problem, did not leave detailed explanations. It was assumed that he was guided by the Golden Ratio (1,618...), but the exact measurements of the figure did not correspond to this.

Now McSweeney claims that the clue is in the triangle. He discovered that Da Vinci had drawn an equilateral triangle between the figure's legs. This element, the analysis showed, corresponds to a well-known concept in dentistry, the Bonville triangle, which defines the ideal jaw position and balance point for chewing.

The author believes that it is the repetition of an equilateral triangle six times around the centre of the body (navel) that makes it possible to obtain ideal proportions. In this case, the side of the square is related to the radius of the inscribed circle in a proportion of about 1.64-1.65 - extremely close to the number 1.633, which is found in nature as an indicator of effective spatial organisation.

"Leonardo's geometric design essentially encoded fundamental spatial patterns in the human body, demonstrating the incredible precision of his Renaissance vision of harmony between anatomy and natural order," Mac Sweeney writes in his article.

He emphasises that the figure in the drawing fits into the pattern of the so-called tetrahedral architecture, a structure often found in the human skull that provides maximum stability and force transmission when chewing.

The discovery, according to the author, not only closes a long-standing academic mystery, but may also have practical implications. The research could influence the design of new prostheses, methods of maxillofacial surgery and even the architecture of future bionic systems.