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

  1. starfish
  2. names
  3. yellow
  4. 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

  1. algebra
  2. answer
  3. capital
  4. combined
  5. difference
  6. dot
  7. effect
  8. ends
  9. letters
  10. names
  11. order
  12. records
  13. rotated
  14. rotates
  15. rotation
  16. rotations
  17. sixth
  18. starfish
  19. symmetries
  20. table
  21. turn
  22. work
  23. yellow