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This image of the Vitruvian Man,[br]taken from Leonardo's sketches,

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has become one of the most recognizable[br]symbols of the Renaissance.

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But why?

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It's a simple pen and ink drawing, right?

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Wrong!

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Let's start to answer this question[br]with a math problem.

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I know how to calculate[br]the area of a circle.

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I take the value for pi[br]and multiply it by the radius squared.

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I also know how to take[br]the area of a square.

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I multiply the base by itself.

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But how can I take the area of a circle[br]and create a square with an equal area?

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This is a problem[br]often called "squaring a circle"

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that was first proposed[br]in the ancient world.

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And like many ideas of the ancient world,

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it was given new life[br]during the Renaissance.

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As it turns out, this problem[br]is impossible to solve

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because of the nature of pi,

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but that's another story.

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Leonardo's sketch,

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which is influenced by the writings[br]of the Roman architect, Vitruvius,

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places a man firmly at the center[br]of a circle and a square.

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Vitruvius claimed the navel[br]is the center of the human body

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and that if one takes a compass[br]and places the fixed point on the navel,

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a circle can be drawn[br]perfectly around the body.

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Additionally, Vitruvius recognized[br]that arm span and height

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have a nearly perfect correspondence[br]in the human body,

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thus placing the body[br]perfectly inside a square as well.

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Leonardo used the ideas of Vitruvius

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to solve the problem[br]of squaring a circle metaphorically

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using mankind as the area for both shapes.

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Leonardo wasn't just thinking[br]about Vitruvius, though.

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There was an intellectual movement[br]in Italy at the time called Neoplatonism.

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This movement took an old concept[br]from the 4th century

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developed by Plato and Aristotle,

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called "The Great Chain of Being."

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This belief holds that the universe[br]has a hierarchy resembling a chain,

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and that chain starts at the top with God,

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then travels down through the angels,[br]planets, stars, and all lifeforms

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before ending with demons and devils.

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Early in this philosophic movement,

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it was thought that mankind's place[br]in this chain was exactly in the center.

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Because humans have a mortal body[br]accompanied by an immortal soul,

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we divide the universe nicely in half.

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Around the time Leonardo[br]sketched the Vitruvian Man, however,

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a Neoplatonist named Pico Della Mirandola[br]had a different idea.

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He pried mankind off the chain

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and claimed that humans[br]have a unique ability

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to take any position they want.

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Pico claimed that God desired[br]a being capable of comprehending

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the beautiful and complicated[br]universe he had created.

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This led to the creation of mankind,

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which he placed[br]at the center of the universe

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with the ability[br]to take whatever form he pleases.

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Mankind, according to Pico,

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could crawl down the chain[br]and behave like an animal

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or crawl up the chain[br]and behave like a god,

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it's our choice.

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Looking back at the sketch,

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we can see that by changing[br]the position of the man,

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he can fill the irreconcilable areas[br]of a circle and a square.

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If geometry is the language[br]the universe is written in,

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then this sketch seems to say[br]we can exist within all its elements.

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Mankind can fill whatever shape[br]he pleases geometrically

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and philosophically as well.

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In this one sketch,[br]Leonardo was able to combine

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the mathematics, religion,[br]philosophy, architecture,

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and artistic skill of his age.

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No wonder it has become such an icon[br]for the entire time period.