full transcript

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 sbolyms of the Renaissance. But why? It's a spilme 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 caleld "squaring a circle" that was first propseod in the ancient wolrd. And like many ieads of the acnenit world, it was given new life during the Renaissance. As it turns out, this problem is impossible to sovle because of the nratue of pi, but that's another story. Leonardo's stkech, which is influenced by the wnritgis 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 pniot on the navel, a circle can be drawn perfectly around the body. aioandldtliy, Vitruvius recognized that arm span and height have a nearly perfect correspondence in the human body, thus placing the body peferlcty 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. loandreo wasn't just thinking about Vitruvius, though. There was an intellectual movement in Italy at the time called Neoplatonism. This momeevnt took an old concept from the 4th century developed by ptalo and Aristotle, called "The graet Chain of Being." This belief holds that the universe has a hrarchiey resembling a chain, and that chain starts at the top with God, then tvrelas down through the angels, planets, stars, and all lmirffoes 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 ceetnr. Because haumns have a mortal body accompanied by an imtamorl soul, we divide the universe nilcey in half. Around the time Leonardo sketched the vuiitravn 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 cdimenerphnog 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 cwral up the chain and behave like a god, it's our cchoie. Looking back at the sketch, we can see that by changing the position of the man, he can fill the irlenibrccaole areas of a circle and a sauqre. If geometry is the language the universe is wtiretn in, then this sketch seems to say we can eixst 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, reiiolgn, philosophy, architecture, and artistic skill of his age. No wonder it has become such an icon for the einrte time period.

Open Cloze

This image of the Vitruvian Man, taken from Leonardo's sketches, has become one of the most recognizable _______ of the Renaissance. But why? It's a ______ 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 ______ "squaring a circle" that was first ________ in the ancient _____. And like many _____ of the _______ world, it was given new life during the Renaissance. As it turns out, this problem is impossible to _____ because of the ______ of pi, but that's another story. Leonardo's ______, which is influenced by the ________ 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 _____ on the navel, a circle can be drawn perfectly around the body. ____________, Vitruvius recognized that arm span and height have a nearly perfect correspondence in the human body, thus placing the body _________ 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. ________ 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 developed by _____ and Aristotle, called "The _____ Chain of Being." This belief holds that the universe has a _________ resembling a chain, and that chain starts at the top with God, then _______ down through the angels, planets, stars, and all _________ 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 ______. Because ______ have a mortal body accompanied by an ________ soul, we divide the universe ______ 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 _____________ 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 _____ 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 ______________ areas 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 elements. Mankind can fill whatever shape he pleases geometrically and philosophically as well. In this one sketch, Leonardo was able to combine the mathematics, ________, philosophy, architecture, and artistic skill of his age. No wonder it has become such an icon for the ______ time period.

Solution

  1. sketch
  2. movement
  3. lifeforms
  4. exist
  5. ancient
  6. point
  7. additionally
  8. solve
  9. leonardo
  10. nature
  11. writings
  12. comprehending
  13. square
  14. nicely
  15. entire
  16. proposed
  17. crawl
  18. immortal
  19. religion
  20. travels
  21. simple
  22. plato
  23. perfectly
  24. irreconcilable
  25. ideas
  26. great
  27. humans
  28. center
  29. vitruvian
  30. called
  31. symbols
  32. hierarchy
  33. world
  34. choice
  35. written

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

  1. ability
  2. accompanied
  3. additionally
  4. age
  5. ancient
  6. angels
  7. animal
  8. answer
  9. architect
  10. architecture
  11. area
  12. areas
  13. aristotle
  14. arm
  15. artistic
  16. base
  17. beautiful
  18. behave
  19. belief
  20. body
  21. calculate
  22. called
  23. capable
  24. center
  25. century
  26. chain
  27. changing
  28. choice
  29. circle
  30. claimed
  31. combine
  32. compass
  33. complicated
  34. comprehending
  35. concept
  36. correspondence
  37. crawl
  38. create
  39. created
  40. creation
  41. della
  42. demons
  43. desired
  44. developed
  45. devils
  46. divide
  47. drawing
  48. drawn
  49. early
  50. elements
  51. entire
  52. equal
  53. exist
  54. fill
  55. firmly
  56. fixed
  57. form
  58. geometrically
  59. geometry
  60. god
  61. great
  62. height
  63. hierarchy
  64. holds
  65. human
  66. humans
  67. icon
  68. idea
  69. ideas
  70. image
  71. immortal
  72. impossible
  73. influenced
  74. ink
  75. intellectual
  76. irreconcilable
  77. italy
  78. language
  79. led
  80. leonardo
  81. life
  82. lifeforms
  83. man
  84. mankind
  85. math
  86. mathematics
  87. metaphorically
  88. mirandola
  89. mortal
  90. movement
  91. multiply
  92. named
  93. nature
  94. navel
  95. neoplatonism
  96. neoplatonist
  97. nicely
  98. pen
  99. perfect
  100. perfectly
  101. period
  102. philosophic
  103. philosophically
  104. philosophy
  105. pi
  106. pico
  107. place
  108. places
  109. placing
  110. planets
  111. plato
  112. pleases
  113. point
  114. position
  115. pried
  116. problem
  117. proposed
  118. question
  119. radius
  120. recognizable
  121. recognized
  122. religion
  123. renaissance
  124. resembling
  125. roman
  126. shape
  127. shapes
  128. simple
  129. sketch
  130. sketched
  131. sketches
  132. skill
  133. solve
  134. soul
  135. span
  136. square
  137. squared
  138. squaring
  139. stars
  140. start
  141. starts
  142. story
  143. symbols
  144. takes
  145. thinking
  146. thought
  147. time
  148. top
  149. travels
  150. turns
  151. unique
  152. universe
  153. vitruvian
  154. vitruvius
  155. world
  156. writings
  157. written