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• This image of the Vitruvian Man,

• taken from Leonardo's sketches,

• has become one of the most recognizable

• symbols of the Renaissance.

• But why?

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

• Wrong!

• Let's start to answer this question

• with a math problem.

• I know how to calculate the area of a circle.

• I take the value for pi

• and multiply it by the radius squared.

• I also know how to take the area of a square.

• I multiply the base by itself.

• But how can I take the area of a circle

• and create a square with an equal area?

• This is a problem often called "squaring a circle"

• that was first proposed in the ancient world.

• And like many of ideas of the ancient world,

• it was given new life during the Renaissance.

• As it turns out,

• this problem is impossible to solve

• because of the nature of pi,

• but that's another story.

• Leonardo's sketch,

• which is influenced by the writings

• of the Roman architect, Vitruvius,

• places a man firmly at the center

• of a circle and a square.

• Vitruvius claimed 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.

• that arm span and height

• have a nearly perfect correspondence in the human body,

• thus placing the body perfectly inside a square as well.

• Leonardo used the ideas of Vitruvius

• to solve the problem of squaring a circle metaphorically

• using mankind as the area for both shapes.

• Leonardo wasn't just thinking about Vitruvius, though.

• There was an intellectual movement

• in Italy at the time

• called Neoplatonism.

• This movement took an old concept

• from the 4th century developed by Plato and Aristotle,

• called "The Great Chain of Being".

• This belief holds that the universe is 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 place in this chain

• was exactly in the center.

• Because humans have a mortal body

• accompanied by an immortal soul,

• we divide the universe nicely in half.

• Around the time Leonardo sketched

• the Vitruvian Man, however,

• a Neoplatonist named Pico della Mirandola

• He pried mankind off the chain

• and claimed that humans have a unique ability

• to take any position they want.

• Pico claimed that God desired

• a being capable of comprehending

• the beautiful and complicated universe he had created.

• This led to the creation of mankind,

• which he placed at the center of the universe

• with the ability to take whatever form he pleases.

• Mankind, according to Pico,

• could crawl down the chain and behave like an animal

• or crawl up the chain and behave like a god,

• it's our choice.

• Looking back at the sketch,

• we can see that by changing the position of the man,

• he can fill the irreconcilable areas

• of a circle and a square.

• If geometry is the language the universe is written in,

• then this sketch seems to say

• we can exist within all its elements.

• Mankind can fill whatever shape

• and philosophically as well.

• In this one sketch,

• Leondardo was able to combine

• the mathematics,

• religion,

• philosophy,

• architecture,

• and artistic skill of his age.

• No wonder it has become such an icon

• for the entire time period.

This image of the Vitruvian Man,

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B1 TED-Ed mankind chain leonardo circle sketch

# 【TED-Ed】Da Vinci's Vitruvian Man of math - James Earle

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阿多賓 posted on 2014/04/24
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