Fibonacci

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by Sierra Christopher13 views·Updated Mar 9, 2020
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Information gathered from: https://math.temple.edu/~reich/Fib/fibo.html https://www.britannica.com/biography/Fibonacci

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  1. Hello. Today I'm gonna be talking about Fibonacci and a
  2. little bit of his background, including one of his greatest
  3. discoveries, which is the Fibonacci sequence.
  4. So the life of Fibonacci.
  5. In his early life, he was born as Leonardo Pizano,
  6. estimated to be born in the year 1170 in Pisa,
  7. and died sometime after 12 40.
  8. He's best known for his work on Indian and Arabian
  9. mathematics and also for being the author of Liver A
  10. Bochy Book of AP Abacus, written in 12 02 In
  11. his early life, during his childhood, he was, um, in
  12. North African port of Boo JIA, which was because his
  13. father was a piece in Merchant.
  14. So there he was able to study calculation with an
  15. Arab master, which, um created his love for math in
  16. his early life.
  17. Later in his life, he then went to Egypt, Greece,
  18. Syria, Sicilian Province to study different new miracle systems.
  19. His book, Libera Bochy Ah, The 1st 7 chapters are
  20. a notation explaining the principle of place value by which
  21. the position of the figure determines whether it is a
  22. unit of 10 100 so forth and demonstrating the use
  23. of numerals in arithmetic Earth medical operations.
  24. Um, I got this from Britannica online about Fibonacci, but
  25. he was able to learn that while he was studying
  26. from Arab masters and these were useful for people like
  27. Fibonacci and his father for profit margin bartering and money
  28. changing eso using and being able to determine whether it
  29. was a unit of 10 or 100 so for so
  30. forth was, um, very useful for money changing in bartering
  31. the number theory was another one of the things that
  32. he was able to accomplish during his lifetime.
  33. Frederick, the second was interested in his riding in math
  34. abilities. So he over invited him over for dinner parties
  35. with other mathematicians and other scholars so that he can
  36. teach them about what he is studying what he's working
  37. on. Um, he then later dedicated his book Libre call
  38. Auditorium or the book of number square numbers to him
  39. in 12 25.
  40. So, as you can see, he had a big impact
  41. on his life and tragic the second was able to
  42. support him.
  43. Ah, lot.
  44. Um, the number theory is basically it's systematic arrangement of
  45. fear ins in which he used his own proves to
  46. work out the problem.
  47. So that means he was able to prove his own,
  48. um, theories and able to show the work through this
  49. number theory.
  50. Um, one of the things that is most creative that
  51. he's done are seen to be most creative is congruent
  52. numbers. Those are numbers that give the same remainder when
  53. divided by a given number.
  54. So he also found an equation that's important to determine
  55. the area of right triangles, which is X squared plus
  56. y squared and X squared minus Weisberg.
  57. So those are both very important in today's mathematical situations.
  58. Uhm, now we're gonna look at something called the Fibonacci
  59. sequence s O.
  60. This is something that we learned about in class.
  61. So this is the same guy.
  62. He created the sequence, and it's kind of complicated, but
  63. also very simple at the same time.
  64. So it all started with this idea.
  65. This is taken from the Fibonacci, um, taken from this
  66. one of an article written about Fibonacci.
  67. Um, it says he said if a pair of rabbits
  68. is placed in an enclosed area, how many rabbits will
  69. be born there?
  70. If we assume that Every month a pair of rabbits
  71. produces another pair in that rabbit begins to very young
  72. two months after their birth.
  73. So assuming that everything goes correctly and registration period is
  74. one month, um, he's asking this question.
  75. So let's look at a little bit of how it
  76. works. So there's a lot of information on this page,
  77. but it is all useful.
  78. So how it works is simplified model under perfect conditions.
  79. As I said, Looks like this, um, using amoebas.
  80. So instead of the rabbits were just using amoebas.
  81. Let's say they split after the same period of growth.
  82. So wanna move A becomes 22 becomes four, then 8
  83. 16 32 and so on.
  84. We get a doubling sequence in the recursive formula of
  85. A N equals two times A and, um so the
  86. pattern we see here is that each cohort or generation
  87. remains as a part of the next, and in addition,
  88. each grow up a pair that contributes to a baby
  89. pair. The number of such baby pairs matches a total
  90. of pears in the previous generation.
  91. Symbolically, F N equals the number of pairs during each
  92. month. Um, n f n equals F n minus one
  93. plus f n minus two.
  94. So, again, um, the pattern that we see here is
  95. each cohort or generation remains a part of the next
  96. in. In addition, each grown up here contributes a baby
  97. care, so that's important to the Fibonacci sequence.
  98. And so we have a recursive formula where each generation
  99. is defined in terms of two previous generation of the
  100. previous two generations.
  101. Using this approach, weaken set, successfully calculate f n forest
  102. many generations as we'd like.
  103. Esso. Basically, how this ends up working out is it
  104. looks somewhat like a spiral on and were able to
  105. kind of see the effect of what starts as to
  106. in under perfect conditions goes on in.
  107. After a period of time, we're able to see what
  108. generations look like.
  109. Um, so that is Fibonacci and his biography, including one
  110. couple of his most important mathematical feats