A British dentist managed to resolve an ancient mathematical enigma hidden within the famous ‘Vitruvian Man’ depiction, created by Leonardo da Vinci. According to this finding, the legendary artwork displays the very same architectural principle that consistently appears in natural forms, Phys.org reports.
The drawing, produced by the renowned Italian master around 1490, is a sketch of a male figure in different stances, concurrently fitted inside a circle and a square. This work was part of Leonardo’s scientific focus on exploring the harmony of human dimensions, partly informed by the writings of the ancient engineer Marcus Vitruvius Pollio, who maintained that body symmetry resembles the architecture of a temple.
Although Vitruvius suggested the concept of aligning figures within circular and rectangular shapes, the actual methodology for achieving such an outcome remained obscure. Da Vinci visualized this concept but left no personal explanation. For over half a millennium, scholars puzzled over how the master attained such precise alignment of all drawing elements, spawning various theories, including the popular golden ratio hypothesis. However, all such theories proved merely approximate and failed to account for the figure’s actual measurements.
This is a fuller vector balance diagram—four hexagons intersecting at a 60-degree angle. They establish a perfect tensegrity structure where forces are ideally balanced around a central point, forming a sphere. This configuration is optimal for uniform spatial distribution.
Now, thanks to the research of London dentist Rory Mc Sweeney, a convincing version for solving the puzzle has been presented for the first time. The specialist uncovered a previously unnoticed characteristic in the ‘Vitruvian Man’ composition: an equilateral triangle formed by the man’s lower legs, marked by the artwork’s creator in accompanying notes. This element parallels another well-known equilateral triangle in medicine, termed ‘Bonwill’s triangle.’ The latter plays a crucial role in dental anatomy and jaw physiology.
The human skull is constructed upon a tetrahedral and triangular scheme, ensuring maximum strength. Bonwill’s triangle connects the lower jaw joints and the front teeth, while the circle and the curve of Spee define the optimal positioning for teeth and occlusion. This scheme boosts the efficiency of chewing motions and confirms the significance of tetrahedrons in human anatomy.
Applying the discovered triangle permitted the calculation of the precise ratio between the square’s side and the circle’s radius, close to the value 1.64–1.65. These figures astoundingly match the universal coefficient used for constructing optimal structures in living nature, approximately equaling 1.633. In Mc Sweeney’s view, such an equivalence is not accidental but proof of da Vinci’s profound grasp of organismal principles long before modern sciences developed.
A hexagonally closely packed structure of spheres, illustrating the mathematical foundation embedded in Leonardo’s geometric system.
“Leonardo’s geometric construction successfully embodied fundamental spatial ratios in the human form, demonstrating the striking accuracy of his Renaissance vision of the mathematical unity between the human figure and the natural order,” the article’s author states.
Mc Sweeney’s discovery is significant not just for satisfying historical curiosity but also for opening prospects for novel approaches in dentistry, orthopedics, and facial plastic surgery. It also stimulates scientific interest in seeking hidden regularities within Renaissance art that might lead to new scientific insights.
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