full transcript

From the Ted Talk by Arthur Benjamin: The magic of Fibonacci numbers

Unscramble the Blue Letters


Now let me ask you a simple question: what is the area of the rectangle? Well, on the one hand, it's the sum of the areas of the srqueas inside it, right? Just as we created it. It's one squared plus one squared plus two squared plus three squared plus five squared plus eight squared. Right? That's the area. On the other hand, because it's a rlnactgee, the area is equal to its height teims its base, and the height is clearly eight, and the base is five plus eight, which is the next Fibonacci number, 13. Right? So the area is also eight times 13. Since we've correctly calculated the area two different ways, they have to be the same nmuber, and that's why the squares of one, one, two, three, five and eight add up to eight times 13.

Open Cloze


Now let me ask you a simple question: what is the area of the rectangle? Well, on the one hand, it's the sum of the areas of the _______ inside it, right? Just as we created it. It's one squared plus one squared plus two squared plus three squared plus five squared plus eight squared. Right? That's the area. On the other hand, because it's a _________, the area is equal to its height _____ its base, and the height is clearly eight, and the base is five plus eight, which is the next Fibonacci number, 13. Right? So the area is also eight times 13. Since we've correctly calculated the area two different ways, they have to be the same ______, and that's why the squares of one, one, two, three, five and eight add up to eight times 13.

Solution


  1. squares
  2. times
  3. number
  4. rectangle

Original Text


Now let me ask you a simple question: what is the area of the rectangle? Well, on the one hand, it's the sum of the areas of the squares inside it, right? Just as we created it. It's one squared plus one squared plus two squared plus three squared plus five squared plus eight squared. Right? That's the area. On the other hand, because it's a rectangle, the area is equal to its height times its base, and the height is clearly eight, and the base is five plus eight, which is the next Fibonacci number, 13. Right? So the area is also eight times 13. Since we've correctly calculated the area two different ways, they have to be the same number, and that's why the squares of one, one, two, three, five and eight add up to eight times 13.

Frequently Occurring Word Combinations


ngrams of length 2

collocation frequency
fibonacci numbers 5
fibonacci number 2


Important Words


  1. add
  2. area
  3. areas
  4. base
  5. calculated
  6. correctly
  7. created
  8. equal
  9. fibonacci
  10. hand
  11. height
  12. number
  13. rectangle
  14. simple
  15. squared
  16. squares
  17. sum
  18. times
  19. ways