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.

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

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