TedTest

From the Ted Talk by James Earle: Da Vinci's Vitruvian Man of math

Unscramble the Blue Letters

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 ridaus 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 pbolerm often cellad "squaring a circle" that was first ppooresd in the ancient world. And like many iades of the ancient world, it was given new life during the Renaissance. As it tnurs out, this problem is ipsbislome to solve because of the nature of pi, but that's another story. Leonardo's sketch, which is ilnceunefd by the writings of the Roman architect, Vitruvius, plcaes 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 dwran perfectly around the body. Additionally, Vitruvius rienceozgd that arm span and height have a nearly perfect correspondence in the hmuan body, thus placing the body perfectly inside a square as well. lnaodero used the ideas of vuiiruvts to solve the problem of squaring a circle metaphorically using mniknad 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 mveenomt took an old concept from the 4th century depeloved by Plato and aitsrotle, called "The Great Chain of Being." This belief holds that the universe has a hierarchy resembling a cihan, and that chain starts at the top with God, then travels down through the angels, paeltns, stars, and all lifeforms before ending with demons and dviels. Early in this philosophic movement, it was thought that mankind's place in this chain was exactly in the cteenr. Because humans have a mortal body accompanied by an immortal soul, we divide the universe nicely in half. Around the time Leonardo sketched the vrtvuaiin 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 ctoerian 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 cichoe. Looking back at the sketch, we can see that by changing the position of the man, he can fill the irreconcilable aares of a circle and a sraque. If geometry is the language the universe is wtriten in, then this sketch seems to say we can eixst within all its ementles. Mankind can fill whatever shpae 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.

Open Cloze

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 ______ 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 _______ often ______ "squaring a circle" that was first ________ in the ancient world. And like many _____ of the ancient world, it was given new life during the Renaissance. As it _____ out, this problem is __________ to solve because of the nature of pi, but that's another story. Leonardo's sketch, which is __________ by the writings of the Roman architect, Vitruvius, ______ 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 _____ perfectly around the body. Additionally, Vitruvius __________ that arm span and height have a nearly perfect correspondence in the _____ body, thus placing the body perfectly inside a square as well. ________ used the ideas of _________ to solve the problem of squaring a circle metaphorically using _______ 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 ________ took an old concept from the 4th century _________ by Plato and _________, called "The Great Chain of Being." This belief holds that the universe has a hierarchy resembling a _____, and that chain starts at the top with God, then travels down through the angels, _______, stars, and all lifeforms before ending with demons and ______. Early in this philosophic movement, it was thought that mankind's place in this chain was exactly in the ______. Because humans have a mortal body accompanied by an immortal soul, we divide the universe nicely in half. Around the time Leonardo sketched the _________ 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 ________ 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 ______. Looking back at the sketch, we can see that by changing the position of the man, he can fill the irreconcilable _____ of a circle and a ______. If geometry is the language the universe is _______ in, then this sketch seems to say we can _____ within all its ________. Mankind can fill whatever _____ 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.

Solution

developed
places
exist
recognized
problem
square
drawn
called
leonardo
influenced
choice
ideas
aristotle
planets
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chain
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vitruvian
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written
mankind
radius
vitruvius
proposed
devils
elements
turns
shape

Original Text

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.

Frequently Occurring Word Combinations

Important Words

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