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Why Math?

Why Math?. Pursuing, extending, and refining an idea, just because one can. F(n) = n 2. If n = 2, F(n) = 4 If n = 3, F(n) = 9 If n = 4, F(n) = 16 …. Iterating F(n) = n 2. If n = 2, F(n) = 4 If n = 4 , F(n) = 16 If n = 16 , F(n) = 256 ….

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Why Math?

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  1. Why Math? Pursuing, extending, and refining an idea, just because one can.

  2. F(n) = n2 • If n = 2, F(n) = 4 • If n = 3, F(n) = 9 • If n = 4, F(n) = 16 • …

  3. Iterating F(n) = n2 • If n = 2, F(n) = 4 • If n = 4, F(n) = 16 • If n = 16, F(n) = 256 • …

  4. Too prosaic! Math is not just about numbers • What if we put a line into the machine and got out a bent line?

  5. V(—) = 22°

  6. V(—) = 22°

  7. V( ) =

  8. V( ) =

  9. V( ) =

  10. V3(—) 22°

  11. V4(—) 22°

  12. V5(—) 22°

  13. V6(—) 22°

  14. V10(—) 22° A cauliflower?

  15. V10(—) 26° Or broccoli?

  16. V10(—) 30°

  17. V10(—) 33°

  18. V10(—) 45°

  19. V10(—) 30°

  20. V10(—) 26°

  21. V10(—) 22°

  22. V10(—) 18°

  23. V10(—) 14° A muffin?

  24. V10(—) 10°

  25. Branching • B( ) = • B( ) =

  26. A bent line

  27. B( )

  28. B2 ( )

  29. B2 ( )

  30. B3 ( )

  31. B4 ( )

  32. B5 ( )

  33. Roots?

  34. Bronchi?

  35. Why these shapes? • Trees? Bronchi? Blood vessels? Roots? • Even broccoli and the tops of muffins? • Why not cats, pigs, and elephants?

  36. And why are these so convincing? • Does the fact that they look right actually tell us anything about reality? Or is this just “coincidence”?Remember… …people see bears in the stars!

  37. Mathematical ways of thinking…

  38. An insight from mathematics • A very intricate structure can arise from an extremely simple rule. • DNA for “complicated” shapes?

  39. Curiosity, ideas, and imagination • Mathematics can help us answer questions… • …but it can also help us ask them.

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