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

- definition
- great
- space
- lines
- 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

- answer
- characterize
- concept
- define
- definition
- draw
- euclid
- euclidean
- flat
- formalist
- formalize
- geometry
- great
- hyperbolic
- impossible
- kinds
- knew
- line
- lines
- mathematicians
- meet
- original
- parallel
- point
- properties
- question
- sense
- shout
- space
- spherical
- structure