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Mystery of Fibonacci numbers

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Mystery of Fibonacci numbers

  1. 1. Introduction  Italian mathematician Leonardo Pisano Fibonacci is known for the Fibonacci number sequence.
  2. 2. Fibonacci Numbers Golden Ratio 1+1 2 1+1 2 ----- 1+2 3 1+2 3/2 1.5 2+3 5 2+3 5/3 1.666 3+5 8 3+5 8/5 1.6 5+8 13 5+8 13/8 1.625 8 + 13 21 8 + 13 21/13 1.615 13 + 21 34 13 + 21 34/21 1.619 21 + 34 55 21 + 34 55/34 1.618 34 + 55 89 34 + 55 89/55 1.618 55 + 89 144 55 + 89 144/89 1.618
  3. 3. In Real World …  In nature  The number of petals on a flower tend to be a Fibonacci number.
  4. 4. In Real World …  Leaves are also found in groups of Fibonacci numbers.  Branching plants always branch off into groups of Fibonacci numbers.
  5. 5. In Real World …  In music  The intervals between keys on a piano are Fibonacci numbers.
  6. 6. In Real World …  In human body  The lengths of bones in a hand are Fibonacci numbers.
  7. 7. Golden Ratio In Website Design  Golden Ratio = Divine Proportion  Discovered in ancient architectural design and is still used today in architecture and design.  If we want to design website for 800x600 resolution monitor than I’ll make my width 760px.  760 divided by 1.62 is 469.14 or 469  Subtract the main column width from the whole width. This will give you the second column width. 760 - 469 = 291.
  8. 8. In Real World …  Face Of Monalisa  People have shown that all things of great beauty have a ratio in their dimensions of a number around 1.618
  9. 9. Think & Give Answer  Suppose a newly-born pair of rabbits, one male, one female, are put in a field.  Rabbits are able to mate at the age of one month. So at the end of its second month a female can produce another pair of rabbits.  Suppose that our rabbits never die. And the female always produces one new pair (one male, one female) every month from the second month on.  How many pairs will there be in one year?

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