full transcript

From the Ted Talk by Scott Rickard: The beautiful math behind the world's ugliest music

Unscramble the Blue Letters


When you talk about the legacy that you leave ... Of course, he couldn't have even anticipated the way that his mathietacms would be used. Thankfully, his mathematics was eventually published. Solomon Golomb realized that that was exactly the mathematics needed to solve the problem of cinreatg a pattern-free structure. So he sent a leettr back to John saying, "It turns out you can generate these patterns using pmrie number theory." And John went about and solved the sonar problem for the Navy.

So what do these patterns look like again? Here's a petratn here. This is an 88-by-88-sized Costas array. It's generated in a very simple way. Elementary school mathematics is sufficient to solve this problem. It's generated by repeatedly multiplying by the nbmeur three: 1, 3, 9, 27, 81, 243 ... When I get to a number that's laregr than 89 which happens to be prime, I keep taking 89s away until I get back below. And this will eventually fill the entrie grid, 88 by 88. There hepapn to be 88 notes on the piano. So today, we are going to have the world premiere of the world's first pattern-free piano sonata.

Open Cloze


When you talk about the legacy that you leave ... Of course, he couldn't have even anticipated the way that his ___________ would be used. Thankfully, his mathematics was eventually published. Solomon Golomb realized that that was exactly the mathematics needed to solve the problem of ________ a pattern-free structure. So he sent a ______ back to John saying, "It turns out you can generate these patterns using _____ number theory." And John went about and solved the sonar problem for the Navy.

So what do these patterns look like again? Here's a _______ here. This is an 88-by-88-sized Costas array. It's generated in a very simple way. Elementary school mathematics is sufficient to solve this problem. It's generated by repeatedly multiplying by the ______ three: 1, 3, 9, 27, 81, 243 ... When I get to a number that's ______ than 89 which happens to be prime, I keep taking 89s away until I get back below. And this will eventually fill the ______ grid, 88 by 88. There ______ to be 88 notes on the piano. So today, we are going to have the world premiere of the world's first pattern-free piano sonata.

Solution


  1. happen
  2. letter
  3. creating
  4. larger
  5. entire
  6. number
  7. prime
  8. mathematics
  9. pattern

Original Text


When you talk about the legacy that you leave ... Of course, he couldn't have even anticipated the way that his mathematics would be used. Thankfully, his mathematics was eventually published. Solomon Golomb realized that that was exactly the mathematics needed to solve the problem of creating a pattern-free structure. So he sent a letter back to John saying, "It turns out you can generate these patterns using prime number theory." And John went about and solved the sonar problem for the Navy.

So what do these patterns look like again? Here's a pattern here. This is an 88-by-88-sized Costas array. It's generated in a very simple way. Elementary school mathematics is sufficient to solve this problem. It's generated by repeatedly multiplying by the number three: 1, 3, 9, 27, 81, 243 ... When I get to a number that's larger than 89 which happens to be prime, I keep taking 89s away until I get back below. And this will eventually fill the entire grid, 88 by 88. There happen to be 88 notes on the piano. So today, we are going to have the world premiere of the world's first pattern-free piano sonata.

Frequently Occurring Word Combinations


ngrams of length 2

collocation frequency
solomon golomb 4
world premiere 3
perfect sonar 2
sonar ping 2
john costas 2
costas array 2
perfect ping 2


Important Words


  1. anticipated
  2. array
  3. costas
  4. creating
  5. elementary
  6. entire
  7. eventually
  8. fill
  9. generate
  10. generated
  11. golomb
  12. grid
  13. happen
  14. john
  15. larger
  16. leave
  17. legacy
  18. letter
  19. mathematics
  20. multiplying
  21. navy
  22. needed
  23. notes
  24. number
  25. pattern
  26. patterns
  27. piano
  28. premiere
  29. prime
  30. problem
  31. published
  32. realized
  33. repeatedly
  34. school
  35. simple
  36. solomon
  37. solve
  38. solved
  39. sonar
  40. sonata
  41. structure
  42. sufficient
  43. talk
  44. thankfully
  45. theory
  46. today
  47. turns
  48. world