full transcript
"From the Ted Talk by Marcus du Sautoy: Symmetry, reality's riddle"

#### Unscramble the Blue Letters

So I've given names. The capital letters, A, B, C, D, E, F, are the nmaes for the rotations. B, for example, rotates the little ylolew dot to the B on the strsfaih. And so on. So what if I do B, which is a sxith of a turn, followed by C, which is a third of a turn? Well let's do that. A sixth of a turn, followed by a third of a turn, the combined effect is as if I had just rotated it by half a turn in one go. So the little table here records how the algebra of these symmetries work. I do one followed by another, the answer is it's rotation D, half a turn. What I if I did it in the other order? Would it make any difference? Let's see. Let's do the third of the turn first, and then the sixth of a turn. Of course, it doesn't make any difference. It still ends up at half a turn.

#### Open Cloze

So I've given names. The capital letters, A, B, C, D, E, F, are the **_____** for the rotations. B, for example, rotates the little **______** dot to the B on the **________**. And so on. So what if I do B, which is a **_____** of a turn, followed by C, which is a third of a turn? Well let's do that. A sixth of a turn, followed by a third of a turn, the combined effect is as if I had just rotated it by half a turn in one go. So the little table here records how the algebra of these symmetries work. I do one followed by another, the answer is it's rotation D, half a turn. What I if I did it in the other order? Would it make any difference? Let's see. Let's do the third of the turn first, and then the sixth of a turn. Of course, it doesn't make any difference. It still ends up at half a turn.

#### Solution

- starfish
- names
- yellow
- sixth

#### Original Text

So I've given names. The capital letters, A, B, C, D, E, F, are the names for the rotations. B, for example, rotates the little yellow dot to the B on the starfish. And so on. So what if I do B, which is a sixth of a turn, followed by C, which is a third of a turn? Well let's do that. A sixth of a turn, followed by a third of a turn, the combined effect is as if I had just rotated it by half a turn in one go. So the little table here records how the algebra of these symmetries work. I do one followed by another, the answer is it's rotation D, half a turn. What I if I did it in the other order? Would it make any difference? Let's see. Let's do the third of the turn first, and then the sixth of a turn. Of course, it doesn't make any difference. It still ends up at half a turn.
#### ngrams of length 2

collocation |
frequency |

symmetrical object |
11 |

mathematical language |
4 |

symmetrical objects |
4 |

symmetries interact |
4 |

magic trick |
3 |

turn anticlockwise |
3 |

combined effect |
3 |

#### Important Words

- algebra
- answer
- capital
- combined
- difference
- dot
- effect
- ends
- letters
- names
- order
- records
- rotated
- rotates
- rotation
- rotations
- sixth
- starfish
- symmetries
- table
- turn
- work
- yellow