Fibonacci

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Fibonaccis Numbers

• TIMES3_ Number theory Day4

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I. Fibonaccis Rabbit
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Recursive relations
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How to Get the Ratio
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The n-th term of the Fibonacci Sequence
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The n-th term of the Fibonacci Sequence
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• 1.Multiply two middle numbers
• 2.Double the result. This is one side.
• 3.Multiply the two outer numbers. This is the
  other side.
• 4. The hypotenuse is the sum of squares of the
  two inner numbers.

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III. Identities of Fibonacci Sequence
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IV. Fibonacci Numbers in Nature
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• Examples of golden ratio from the human face
• Center of pupil Bottom of teeth Bottom of
  chin
• Outer inner edge of eye Center of nose
• Outer edges of lips Upper ridges of lips
• Width of center tooth Width of second tooth
• Width of eye Width of iris
• Source lthttp//hynesva.com/blogs/character_and_exc
  ellence/archive/2009/11/15/gt

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• From the entire body
• The human head forms a golden rectangle (width
  height)
• Whole body height head to fingertips
• Top of head to fingertips head to navel and
  elbows
• Top of head to navel and elbows head to
  pectorals and inside top of arms
• Top of head to navel and elbows width of
  shoulders
• Top of head to navel and elbows length of
  forearm
• Top of head to navel and elbows length of
  shinbone
• Top of head to pectorals top of head to base of
  skull
• Top of head to pectorals width of abdomen
• Length of Forearm length of hand

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Q What is the recursive relation of the
Fibonacci sequence?QHow do you get golden
ratio from Fibonacci numbers?