3 beauty marks in the shape of a triangle

this image of the vitruvian man,taken from leonardo's sketches, has become one of the most recognizablesymbols of the renaissance. but why? it's a simple pen and ink drawing, right? wrong! let's start to answer this questionwith a math problem. i know how to calculatethe area of a circle. i take the value for piand multiply it by the radius squared. i also know how to takethe area of a square.

i multiply the base by itself. but how can i take the area of a circleand create a square with an equal area? this is a problemoften called "squaring a circle" that was first proposedin the ancient world. and like many ideas of the ancient world, it was given new lifeduring the renaissance. as it turns out, this problemis impossible to solve because of the nature of pi, but that's another story.

leonardo's sketch, which is influenced by the writingsof the roman architect, vitruvius, places a man firmly at the centerof a circle and a square. vitruvius claimed the navelis the center of the human body and that if one takes a compassand places the fixed point on the navel, a circle can be drawnperfectly around the body. additionally, vitruvius recognizedthat arm span and height have a nearly perfect correspondencein the human body, thus placing the bodyperfectly inside a square as well.

leonardo used the ideas of vitruvius to solve the problemof squaring a circle metaphorically using mankind as the area for both shapes. leonardo wasn't just thinkingabout vitruvius, though. there was an intellectual movementin italy at the time called neoplatonism. this movement took an old conceptfrom the 4th century developed by plato and aristotle, called "the great chain of being." this belief holds that the universehas a hierarchy resembling a chain,

and that chain starts at the top with god, then travels down through the angels,planets, stars, and all lifeforms before ending with demons and devils. early in this philosophic movement, it was thought that mankind's placein this chain was exactly in the center. because humans have a mortal bodyaccompanied by an immortal soul, we divide the universe nicely in half. around the time leonardosketched the vitruvian man, however, a neoplatonist named pico della mirandolahad a different idea.

he pried mankind off the chain and claimed that humanshave a unique ability to take any position they want. pico claimed that god desireda being capable of comprehending the beautiful and complicateduniverse he had created. this led to the creation of mankind, which he placedat the center of the universe with the abilityto take whatever form he pleases. mankind, according to pico,

could crawl down the chainand behave like an animal or crawl up the chainand behave like a god, it's our choice. looking back at the sketch, we can see that by changingthe position of the man, he can fill the irreconcilable areasof a circle and a square. if geometry is the languagethe universe is written in, then this sketch seems to saywe can exist within all its elements. mankind can fill whatever shapehe pleases geometrically

and philosophically as well. in this one sketch,leonardo was able to combine the mathematics, religion,philosophy, architecture, and artistic skill of his age. no wonder it has become such an iconfor the entire time period.