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.

Relat­ed Con­tent:

Down­load the Sub­lime Anato­my Draw­ings of Leonar­do da Vin­ci: Avail­able Online, or in a Great iPad App

Leonar­do da Vinci’s Bizarre Car­i­ca­tures & Mon­ster Draw­ings

How to Build Leonar­do da Vinci’s Inge­nious Self-Sup­port­ing Bridge: Renais­sance Inno­va­tions You Can Still Enjoy Today

Leonar­do da Vinci’s Vision­ary Note­books Now Online: Browse 570 Dig­i­tized Pages

Ralph Steadman’s Wild­ly Illus­trat­ed Biog­ra­phy of Leonar­do da Vin­ci (1983)

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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