Da Vinci’s Vitruvian Man of math – James Earle

Da Vinci’s Vitruvian Man of math – James Earle

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 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
has 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,
Leonardo 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.


  1. Leonard was wrong. Wingspan is slightly greater than height on average. There are gender and race differences. see post on my blog Philosopher UK.com

  2. 对了,哪布有没有比晝更高價??,心血结布畫出??。

  3. Complaints about the narrator… 🤦🏽‍♂️🤦🏽‍♂️ is the dumbest thing you can ever do.. blossom on what he says not on how he says it

  4. Nope! The drawing was actually a solution to an architectural problem. Enough of this Humanities-led pseudo-philosophical babble lol

  5. Narrator sounds like a millennial anti-depressant fed, social media raised, typical NPR type trendy guy.

  6. Da vinci's vinctruvian. Man of math was not finished! If. He live today he would have place the ocean at the bottom. Land on the right side.and air on the left side. And space on top. The vitruvian man of of math is science and science is part of math.

  7. May be Leonardo never thought like this, just created random sketch but these experts do aftermaths and tell us the things which may be Leonardo never thought of LOL

  8. I feel like its a symbol from a 4th dimension.. time. You see different versions of yourself like trying to make a stick man walk or run through a series of flipping pages..

  9. The narrator voice kinda reminded me of Joey Tribbiani's award accepting speech. Not interested to do it, but is doing it anyway.

  10. The Queen of England owns the original drawing, along with a vast portfolio of Da Vinci's drawings, and some paintings.

  11. All this explanation, and I bet you all he did was draw a dude in a square and circle because he was just bored..

  12. man am so sorry to say this, but you sound terrible. the content is alright. please have someone else narrate, thank you.

  13. The channel should choose properly who narrates the story. He sounds so uninterested and rushing narrating the story. Yes, a man can put himself to anything he wants, but it doesn’t mean that he can be good in all of them.

  14. Them: come on it's been so long we have to finish this video tonight at any cost.
    Narrator: let's continue tomorrow I'm too sleepy.
    Them: come on! Let's do it now.
    Narrator: (yawning) ya ok.

  15. I didnt really understand the problem at the base of the video of how to create a square equal to the circle..
    if you know that the circle is pie*R^2=9 and square is B^2=9 just go reverse on the formulas..

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