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The Fibonacci Sequence

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by

Faith Martinmaas

on 17 May 2016

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Transcript of The Fibonacci Sequence

youtube.com/watch?v=gTQeVlDsAi0&sns=em
.
The Fibonacci Sequence


Pingala's Sequence
short syllables = 1 unit
long syllables = 2 units
Sanskrit Prosody (Pingala)

How many combinations can be made from long and short units?
What is the Fibonacci sequence?
It is created by adding the previous integer to the next integer

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811

The Fibonacci sequence can be found all throughout nature
1 unit or
1 syllable
2 units or
2 syllables
the Fibonacci sequence can be seen in the way trees and plants grow

The branches of leaves and plants grow in a pattern called phyllotaxis, which can be expressed as a fraction. These fractions exhibit the Fibonacci sequence.
Units
Combinations
1

2

3

4
The oak tree has a phyllotaxis fraction of 2/5, which means that the pattern uses five branches to spiral two times around the trunk and complete one pattern.
1

2

3

5
Fractions of other trees: elm tree 1/2, beech 1/3, willow 3/8, almond 5/13
One scientific theory is that the Fibonacci growth pattern helps trees collect sunlight more efficiently
.
.

Units
Combinations
n
number n-2
number n-1
f(n) = f(n-2) + f(n-1)
in pine cones the amount of left and right facing spirals correspond to Fibonacci numbers
a similar pattern can be seen in sunflower seeds
this pattern allows the sunflower head to hold the largest amount of seeds in the most efficient way
References
http://www.mensaforkids.org/teach/lesson-plans/fabulous-fibonacci/

http://gipsy.ninja/13-year-old-makes-solar-breakthrough-based-on-the-fibonacci-sequence/

http://www.amnh.org/learn-teach/young-naturalist-awards/winning-essays2/2011-winning-essays/the-secret-of-the-fibonacci-sequence-in-trees/

http://www.research.att.com/articles/featured_stories/2012_03/201203_OEIS.html?fbid=-SmMbw5qTLQ

https://en.wikipedia.org/wiki/Fibonacci_number
Full transcript