The Elegant Mathematics of Vitruvian Man, Leonardo da Vinci’s Most Famous Drawing: An Animated Introduction

Nearly 500 years after his death, we still admire Leonardo da Vinci's many and varied accomplishments in painting, sculpture, architecture, science, and quite a few other fields besides, most of which would have begun with his putting down some part of the formidable contents of his head on to a piece of paper. (As we've seen, sometimes he needed to draw up a to-do list first.) Some of those works remained on paper, and even became famous in that humble form. If you've only seen one of Leonardo's drawings, for instance, it's almost certainly Vitruvian Man.

Leonardo's circa-1490 study of the proportions of the human body — or to put it in more common terms, the picture of the naked fellow standing inside a square and a circle — stands at an intersection of art and mathematics, one at which Leonardo spent a great deal of time throughout his life. The Ted-ED lesson above, written by educator James Earle, gets into "the geometric, religious and philosophical significance of this deceptively simple drawing" whose title references the first-century BCE Roman architect and civil engineer Marcus Vitruvius Pollio, who claimed that "the navel is the center of the human body, and that if one takes a compass and places the fixed point on the navel, a circle can be drawn perfectly around the body."

Vitruvius also realized that "arm span and height have a nearly perfect correspondence in the human body, thus placing the body perfectly inside a square as well." Both he and Leonardo saw real implications in this alignment between anatomy and geography, beginning with the notion that buildings and other works of man should also take on these "perfect" proportions. All of this ties in with the problem, first proposed by ancient geometers, of "squaring the circle," that is, finding a procedure to hand-draw a square and a circle both of equal area. Leonardo used Vitruvian Man to point toward one possible solution using the human body.

You can learn more about the importance and legacy of the drawing in the BBC documentary The Beauty of Diagrams, available on Youtube (part one, part two). "Although the diagram doesn't represent some huge scientific breakthrough," says its host, mathematician Marcus du Sautoy, "it captures an idea: that mathematics underpins both nature and the manmade world. It represents a synthesis of architecture, anatomy, and geometry. But it's the perfection and elegance of Leonardo's solution to this riddle of the square and the circle in Vitruvius which gives the diagram its power and its beauty." And judging by the unabated popularity of Vitruvian Man parodies, it looks to have at least another half-millennium of relevance ahead.

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Based in Seoul, Colin Marshall writes and broadcasts on cities and culture. His projects include the book The Stateless City: a Walk through 21st-Century Los Angeles and the video series The City in Cinema. Follow him on Twitter at @colinmarshall or on Facebook.

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  • David Bradley says:

    …except, of course, that Leonardo abandoned this avenue of reasoning when he realised the perfect proportions he assumed Vitruvius had found were wrong. The diagram, although famous, shows nothing about human anatomy. It’s 500-year old #FakeNews. Just ask the curator of the Queen’s collection of Leonardo da Vinci works…I paraphrase what he told me 5 years ago:

    Roman architect Marcus Vitruvius Pollio who suggested that somehow the perfect man could with arms and legs akimbo transect a perfect circle and a perfect square. In his work, Leonardo measure lengths, ratios and angles but could not find the perfect ratios suggested by Vitruvius 1500 years before. Instead, he obtained odd fractions 5/11’s, 7/17th’s none of which seemed to point to the perfect circle or the perfect man and Leonardo turned back from this dead-end.

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