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

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has become one of the most recognizable
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
with a math problem.

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I know how to calculate
the area of a circle.

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

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I also know how to take
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
and create a square with an equal area?

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This is a problem
often called "squaring a circle"

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that was first proposed
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
during the Renaissance.

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As it turns out, this problem
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
of the Roman architect, Vitruvius,

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

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Vitruvius claimed the navel
is the center of the human body

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

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a circle can be drawn
perfectly around the body.

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Additionally, Vitruvius recognized
that arm span and height

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have a nearly perfect correspondence
in the human body,

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thus placing the body
perfectly inside a square as well.

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Leonardo used the ideas of Vitruvius

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to solve the problem
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
about Vitruvius, though.

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

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This movement took an old concept
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
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,
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
in this chain was exactly in the center.

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

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we divide the universe nicely in half.

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Around the time Leonardo
sketched the Vitruvian Man, however,

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a Neoplatonist named Pico Della Mirandola
had a different idea.

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He pried mankind off the chain

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and claimed that humans
have a unique ability

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to take any position they want.

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Pico claimed that God desired
a being capable of comprehending

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the beautiful and complicated
universe he had created.

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This led to the creation of mankind,

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which he placed
at the center of the universe

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with the ability
to take whatever form he pleases.

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Mankind, according to Pico,

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could crawl down the chain
and behave like an animal

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or crawl up the chain
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
the position of the man,

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

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If geometry is the language
the universe is written in,

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

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Mankind can fill whatever shape
he pleases geometrically

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and philosophically as well.

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In this one sketch,
Leonardo was able to combine

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the mathematics, religion,
philosophy, architecture,

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and artistic skill of his age.

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