What Are the Fibonacci Numbers

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What Are the Fibonacci Numbers?
In other words, whats up with those numbers
being so darn special?

• Erin ODougherty
• 7-15-2008
• History of Numbers

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What are the Fibonacci numbers, exactly?

• The Fibonacci numbers are 1,1,2,3,5,8,13,21,34,55
  ,89,144,233,377,
• 610,987..
• To get them you simply find the sum of the
  previous two consecutive numbers.
• Ex 112
• 213
• 325
• Fibonacci used this sequence of numbers to
  investigate population growth in rabbits. The
  problem goes like this

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So, whats the story?

• Well, it all started with those darn
  rabbits..bored after a long winters break. What
  else were they left to do?
• So, they decided to do what we all do when we get
  bored. And so, we begin our tale.Fibonacci
  decided to try with one newly born pair of
  bunnies (one female and one male), in a beautiful
  field of daises. These two bunnies take one month
  to become sexually mature. At this point they
  produce a new pair of bunnies (always one male
  and one female). If you continued this pattern,
  how many pairs would there be in one year?

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Fibonaccis Bunny Thereom
1,1,2,3,5,..
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The Answer.
After 12 months of this nonsense there will be
377 pairs! This series continues on and on and
on.
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• If it is true, that mathematics is a way of
  making sense in our chaotic world, with a system
  of numbers, then it can be said that Fibonaccis
  numbers are way of making sense of our natural
  world.

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Other Fascinating Things About The Fibonacci
Numbers

• This series does appear in nature quite a bit.
  It can been seen in everything from sunflowers to
  pineapples to pine cones.
• Fibonacci has been closely linked to the arts,
  architecture,natural phenomena, and trigonometry.
  

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Sunflowers
Spiraling outwards from the center of the
sunflower, both clockwise and counterclockwise,
this sunflower displays two consecutive numbers
in the Fibonacci series.
8 and 13
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Pineapples
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Pinecones
This pinecone has 5 and 8 spirals.
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More Cool Things

• The Fibonacci series seems to have a direct
  correlation to the Golden Ratio. As the numbers
  in the sequence increase, their ratio starts to
  hover around 1.61803 which is why Fibonaccis
  numbers are also referred to as the Golden
  Sequence.
• The Golden Ratio also appears in our natural
  world frequently.

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Imagine, if our students applied this outside of
math class

• The above cartoon (Amend 2005) shows an
  unconventional sports application of the
  Fibonacci numbers (left two panels). (The right
  panel instead applies the Perrin sequence).

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Sources

• Mactutor
• http//library.thinkquest.org/27890/altver/applica
  tions4.html
• www.dm.unito.it/.../immagini/Fibonacci.jpg
• http//farm1.static.flickr.com/163/333039205_8eb19
  4ae40.jpg?v0
• http//library.thinkquest.org/27890/media/photoPin
  eapple2.jpg
• http//mathworld.wolfram.com/FibonacciNumber.html
• Katz, V., The History of Mathematics, pp. 282-287
• Livio, M., The Golden Ratio, pp. 94-98