**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://www.vali.de/wp-content/uploads/fibbonaci2.png

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.

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