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TED-Ed 028・・Da Vinci's Vitruvian Man of math 　　　　　　　　　　代表頁に戻る　　　　　　　　　　
　　　　　　　　　（ダ・ヴィンチのウィトルウィウス的人体図に関する数学）

ウィトルウィウス的人体図とは⇒ Wikipediaの解説（日本語）
（描かれている真円ではへそを中心としているが、正方形はへそを中心としておらず、解剖学的に見て正しい）

03分・・200wpm　　　2013/11/24 新出


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.