full transcript
"From the Ted Talk by Margaret Wertheim: The beautiful math of coral"

Unscramble the Blue Letters

So what is this impossible hyperbolic structure? Before hlobyirepc geometry, mathematicians knew about two kinds of space: Euclidean space, and spherical space. And they have different properties. Mathematicians like to characterize things by being formalist. You all have a sense of what a flat sapce is, Euclidean space is. But mathematicians formalize this in a particular way. And what they do is, they do it through the concept of parallel lines. So here we have a line and a point outside the line. And Euclid said, "How can I define parallel liens? I ask the question, how many lines can I draw through the point but never meet the original line?" And you all know the answer. Does someone want to shout it out? One. gaert. Okay. That's our definition of a parallel line. It's a diinfioetn really of Euclidean space.

Open Cloze

So what is this impossible hyperbolic structure? Before __________ geometry, mathematicians knew about two kinds of space: Euclidean space, and spherical space. And they have different properties. Mathematicians like to characterize things by being formalist. You all have a sense of what a flat _____ is, Euclidean space is. But mathematicians formalize this in a particular way. And what they do is, they do it through the concept of parallel lines. So here we have a line and a point outside the line. And Euclid said, "How can I define parallel _____? I ask the question, how many lines can I draw through the point but never meet the original line?" And you all know the answer. Does someone want to shout it out? One. _____. Okay. That's our definition of a parallel line. It's a __________ really of Euclidean space.

Solution

  1. definition
  2. great
  3. space
  4. lines
  5. hyperbolic

Original Text

So what is this impossible hyperbolic structure? Before hyperbolic geometry, mathematicians knew about two kinds of space: Euclidean space, and spherical space. And they have different properties. Mathematicians like to characterize things by being formalist. You all have a sense of what a flat space is, Euclidean space is. But mathematicians formalize this in a particular way. And what they do is, they do it through the concept of parallel lines. So here we have a line and a point outside the line. And Euclid said, "How can I define parallel lines? I ask the question, how many lines can I draw through the point but never meet the original line?" And you all know the answer. Does someone want to shout it out? One. Great. Okay. That's our definition of a parallel line. It's a definition really of Euclidean space.

ngrams of length 2

collocation frequency
straight line 5
global warming 4
square foot 4
foot gallery 4
hyperbolic geometry 4
sea slugs 4
euclidean space 4
original line 4
mathematicians thought 4
coral reef 3
coral reefs 3
hyperbolic space 3

ngrams of length 3

collocation frequency
square foot gallery 4

Important Words

  1. answer
  2. characterize
  3. concept
  4. define
  5. definition
  6. draw
  7. euclid
  8. euclidean
  9. flat
  10. formalist
  11. formalize
  12. geometry
  13. great
  14. hyperbolic
  15. impossible
  16. kinds
  17. knew
  18. line
  19. lines
  20. mathematicians
  21. meet
  22. original
  23. parallel
  24. point
  25. properties
  26. question
  27. sense
  28. shout
  29. space
  30. spherical
  31. structure