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A London-based dentist may have cracked a centuries-old mathematics puzzle hidden in one of the most famous anatomical drawings in the world—Leonardo da Vinci's Vitruvian Man. This discovery suggests the iconic image reflects the same design blueprint frequently found in nature.

The pen-and-ink drawing of a nude male figure in two superimposed poses, with arms and legs enclosed within a circle and a square, was created by the Renaissance polymath around 1490. It is a study of the ideal human form, partly influenced by the writings of Roman architect Marcus Vitruvius Pollio, who believed the human body has harmonious proportions, just like a well-designed temple.

He proposed that a human figure could fit perfectly inside a circle and a square, but provided no mathematical framework for this geometric relationship. Da Vinci solved it but did not explicitly explain how.

For more than 500 years, how he achieved this perfect fit in one of the world's most analyzed drawings has remained a mystery. It's one that has generated numerous theories and ideas, such as the Golden ratio (1.618...). But none have matched the actual measurements.

However, by London-based dentist Rory Mac Sweeney, published in the Journal of Mathematics and the Arts, is finally providing some answers to da Vinci's geometric method.

Hidden triangle

The paper describes a hidden detail in the Vitruvian Man, namely an equilateral triangle between the man's legs referenced in da Vinci's notes for the drawing. Analysis revealed that this shape corresponds to Bonwill's triangle, an imaginary equilateral triangle in dental anatomy that governs the optimal performance of the human jaw.

The use of the triangle in the artwork helped produce a ratio of 1.64 to 1.65 between the square's side and the circle's radius. That's very close to the special blueprint number of 1.633, which is found throughout nature for building the most efficient structures.

Mac Sweeney believes this is no accident and suggests that da Vinci perfectly understood the ideal design of the human body, long before modern science.

"Leonardo's geometric construction successfully encoded fundamental spatial relationships in human form, demonstrating the remarkable precision of his Renaissance vision of mathematical unity between the human figure and natural order."

Mac Sweeney's paper does a lot more than scratch a 500-year-old academic itch. The findings could inspire new approaches in dental anatomy, prosthetic design, and craniofacial surgery. They could also prompt further investigations into Renaissance art for scientific insights that have lain hidden for centuries.

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