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The history of art is full of universal icons, but few, very few, reach the popularity level of the ‘Vitruvio man’ drawn around 1490 by Leonardo da Vinci. And it is logical. Artistic and scientific issues apart, the work has become a reference Pop. The original is preserved in the Accademia di Belle Arti Venice, but the same face, the same body, has stamped over the last decades in books, t -shirts, sweatshirts, backpacks and posters. That without counting every time we have seen it reproduced on the big screen.
The most curious thing is that despite that exhibition, the ‘man of vitruvio’ is still surrounded by mysteries. Or so it was until now, at least. A London dentist believes having solved the complex mathematical puzzle that Leonardo hidden in the work.
A name: Marcus Vitruvius. Leonardo da Vinci’s is (by far) the most famous, but the Tuscan genius was not the only one in representing the man of vitruvio. We keep more or less similar samples from other artists, such as Francesco Di Giorgio Martini either Giacomo Andrea de Ferrara. And it’s normal. After all, these are exercises based on the canon of the human body of Marcus Vitruvius (Exactly, hence his name), a Roman architect and engineer. It was he who many centuries before Leonardo theorized about human physiognomy in Of archiecture.
“In the body, the central point is the navel. If a man placed himself on his back, with extended hands and feet and a compass focused on the nave The architect theorized Roman in the first century before our era, convinced that a man’s proportions can adjust to a square.
But … how to do it? That is the theory. Different thing is practice. Throughout the different artists have launched themselves to represent human physiognomy partially inspired by the canon of proportions proposed by vitrubio. Not everyone with equal fortune. By 1490 Leonardo Da Vinci, who then was around 40, got down to work in one of his notebooks and prepared a drawing that during the last five centuries has fascinated scholars and profane.
The work shows a man in several overlapping positions, standing, with extended legs and more or less open arms. All perfectly registered in a square and in a circle in an exercise that would probably have fascinated the Roman architect. We have recorded the result in memory and a quick search arrives on Google to find good quality reproductions, but there is a pending mystery: how the hell did Leonardo did?
The great ask unknown. Yes, the result is obvious. And yes, the drawing is there for those who want to copy it in detail. But … what recipe Did Vinci continue to plan and execute it? What calculations did you use? Was it based on any pattern? And if so, what system did you employ? “The search for the Da Vinci geometric method has generated numerous theories, each of which tries to explain the measured relationship between the circle and the square in the original drawing,” Explain Rory Mac Sweeney, the British dentist who believes he has found the key.
“For more than 500 years, the Da Vinci geometric system for the precise relationship between the circle and the square in his drawing of the ‘Vitruvio man’ has remained in the mystery,” Mac Sweeney abounds, which has just published An article reviewed by parts in Journal of Maythematics and Arts.
What if the key is the golden proportion? His theory is just that, a theory, but it is interesting because it offers an alternative to the most popular explanation, which argues that to draw his drawing Da Vinci was inspired by the Aurea proportionan idea that reinforces the collaboration of the Tuscan with his compatriot Luca Paciolithe author of Of divine proportion. The problem, Remember Mac Sweeneyis that this explanation has not just been perfect. “It produces a significant error, which seems unlikely given Leonardo’s geometric precision.”
Good riddle, bad explanation. Other authors have provided alternative explanations to the mystery of Vitruvio, such as Leonardo was based on octagons or a heptagon, but Mac Sweeney believes all these theories present “a fundamental problem”: they approach more or less the measures used by the artist in his diagram, but in the opinion of the British researcher it is difficult to connect them with the themes that really obsessed Da Vinci.
“They are still purely abstract mathematical exercises, without connection with Leonardo da Vinci’s documented interest in human anatomy, natural functional and main relationships. As geometric riddles, they work. As explanations of Leonardo’s methodology and intentions, they do not offer a convincing justification of their specific decisions,” Reflect.
Hidden “with the naked eye”. The most curious thing is that Mac Sweeney believes that the solution “has been hidden with the naked eye” in the handwritten annotations left by Leonardo himself next to the drawing. Specifically, it refers to a comment in which the artist points out that, with the body in a certain posture, the space between the legs forms an equilateral triangle. For a long time it was believed that this phrase was a simple poetic ornament, pure rhetoric or a practical guide for composition, but the British expert believes that it is the key to mystery.
And what is special? That the triangle adjusts to a natural pattern, one that Mac Sweeney knows well for his dentist profession: Bonwill’s trianglean imaginary equilateral triangle of the human anatomy that marks the fundamental geometric relationship for the proper functioning of the jaw. “Connects the mandibular condyles with the midpoint of the lower central incisors and corresponds precisely to Leonardo’s explicit reference to an ‘equilateral triangle’ in its construction of the ‘vitruvio man'”, Clarify.
“The construction of Leonardo demonstrates the same tetrahedral principles present in craniofacial architecture,” insists The British dentist before citing studies and calculations that reinforce its hypothesis. “The equilateral triangle, which Leonardo made explicit reference between the legs of the figure, when replicating six times around the navel, creates the hexagonal pattern that generates the measured reason of approximately 1.64 between the side of the square and the radius of the circle.”
Why is it important? For several reasons. From the outset, because if Mac Sweeney is right, he would solve the mystery that has been surrounding Leonardo’s drawing. Secondly because he would show that the Tuscan artist sensed Bonwill’s triangle centuries before he did William Bonwillthe dentist who gave him name in the 19th century. And third, because for the British it opens new approaches beyond history or mathematics and reach dentistry.
Images | Wikipedia 1 and 2 and Journal of Mathematics and the Arts/Rory Mac Sweeney
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