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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.

  • Additionally, Vitruvius recognized

  • 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

  • had a different idea.

  • 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

  • he pleases geometrically

  • 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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