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# Fibonacci Spirals & Maximum Packing

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## Emily Crkvencic

on 30 August 2016

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#### Transcript of Fibonacci Spirals & Maximum Packing

Fibonacci Spirals & Maximum Packing
Maximum Packing
Maximum packing
follows the Fibonacci spiral and the theory of conservation, where there is no vacuum; everything is filled by something.
Rabbits!
The
doubling sequence
occurs when in a sequence the previous number is added to the number before.
So if the the starting number was 2, the next number would be 3.
An example of this can be seen with rabbits.

Works Cited
Temple University. Dan Reich, Web. 10 Nov. 2013. <https://math.temple.edu/~reich/Fib/
fibo.html>.
http://nrich.maths.org/content/id/7668/hand.jpeg
http://farm8.staticflickr.com/7137/7648038846_f5382a5448_z.jpg
http://engage.intel.com/servlet/JiveServlet/showImage/38-3054-4209/fibonac_8.gif
http://4.bp.blogspot.com/-nd8O52oNLj0/TlpbwxzSOSI/AAAAAAAAALc/Nb7nlDejcXg/s1600/FibIrene.png
http://2.bp.blogspot.com/_mZ4x5p0sAZc/TId1_S3HReI/AAAAAAAAGHs/BqgO3OV-ZK4/s1600/ParthenonGoldenRatio.png
http://cdn1.cdnme.se/cdn/8-1/3112931/images/2012/galaxy-fibonacci_192214542.jpg
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibFormula.html

Quiz!
Question 1:
Fibonacci Spiral
The Universe and everything in it exists in a natural balance and
Fibonacci spiral
is the key to this.
The
double sequence
,
maximum packing
, and
proportion
are all based off of this spiral.

Anything from the Milky Way to a building to a hurricane is based off of this pattern.

Emily Crkvencic
The numerical sequence starting at 0 goes as follows:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ...
This sequence goes on forever.
This principle can literally be seen everywhere. A few examples are:
This is also based off of the
Fibonacci spiral
.
Flowers
The seeds and petals follow the spiral to acheive maximum packing
Hands
The finger follows proportion, putting everything at its full potential
Seashells
Their 'design' follows the Fibonacci spiral
The Face
Follows the spiral, making it proportional
What is the number after 89 in the Fibonacci sequence?
55 is the number before, so 233 is the number after it.
Hint: the number before 89 is 55
The Hand
Here is a counter example of a hand that isn't so aesthetically pleasing
Thanks for Watching!
For Mr. MacDonald 's 7th grade Algebra 1 Class
Made by Emily Crkvencic on Prezi
Full transcript