New research published in the Journal of Mathematics and the Arts reveals the hidden mathematical principle behind Leonardo da Vinci's iconic Vitruvian Man drawing. Dr. Rory Mac Sweeney discovered that Leonardo's mention of an "equilateral triangle" between the figure's legs wasn't random—it corresponds to Bonwill's triangle, a principle governing efficient jaw function established in 1864. When Bonwill's triangles are arranged in three-dimensional space according to optimal geometric principles, they naturally create a ratio of 1.633 which is also found throughout nature—in the most efficient way to pack spheres, in crystal structures, and in human skull proportions. Leonardo's actual measured ratio of 1.645 represents a remarkably close approximation to this universal constant of 1.633. The findings suggest Leonardo intuitively understood the same mathematical rules that nature uses for optimal design centuries before modern science, positioning the Vitruvian Man as both artistic masterpiece and scientific breakthrough.
LONDON, July 2, 2025 /PRNewswire-PRWeb/ -- A 500-year-old puzzle over one of the world's most famous drawings, Leonardo da Vinci's Vitruvian Man, appears to have been solved. New research reveals that the secret to how Leonardo perfectly placed the human figure inside a circle and a square was hidden in plain sight within the artist's own notes.
The key, according to a paper in the Journal of Mathematics and the Arts, is Leonardo's specific mention of an "equilateral triangle" drawn between the man's legs. A researcher has discovered this isn't just a random shape. It directly matches a shape found in modern anatomy that governs how our jaws work in the most efficient way, a principle known as "Bonwill's triangle". This suggests Leonardo understood the ideal architecture of the human body centuries before modern science.
When this triangle is used to construct the drawing, it produces a specific ratio, or relationship, between the size of the square and the circle. That ratio is approximately 1.64. Scientists were stunned to find that this number is almost identical to a "special blueprint number" (1.633) that appears again and again in nature for building the strongest, most efficient structures.
This same blueprint number is found in:
- The tightest way to pack spheres, like stacking oranges at the supermarket.
- The atomic structure of super-strong crystals.
- The unique proportions of the human skull.
- The geometry of a perfectly functioning human jaw.
"We've all been looking for a complicated answer, but the key was in Leonardo's own words. He was pointing to this triangle all along," says Dr Rory Mac Sweeney, the study's author. "What's truly amazing is that this one drawing encapsulates a universal rule of nature. Leonardo knew, or sensed, that our bodies are built with the same mathematical elegance as the universe around us."
This discovery is significant because it shows that Vitruvian Man is far more than just a beautiful piece of art. It is a work of scientific genius that was centuries ahead of its time.
By proving that our bodies follow these universal rules of efficient design, this research has significant ramifications for anthropology and human evolution.
Media Contact
Rory Mac Sweeney, Precision Endodontics, 44 7801846111, [email protected], igdp
SOURCE Precision Endodontics
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