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saoirse Mahoney

on 22 September 2015

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Transcript of Fibonacci

Fibonacci In Nature
How does it mimic Fibonacci ?
One example of Fibonacci in nature is the rose (as seen on the previous slide). The rose mimics the golden spiral. The spiral starts out very small and gradually expands as it spirals around. Another example of how nature mimics the fibonacci sequence is, a tree. Its branches mimic the actual fibonacci sequence. Its trunk represents the number one in the sequence. Then its branches split apart into two branches. Those branches split into three and then five, and so on.
What is the Golden Spiral?
The Golden Spiral is when you take the length and width of a rectangle and add it together with another rectangle with the same measurements. Then make a larger rectangle with the previous answer and you keep going.
What is Phi?
What is Fibonacci?
Fibonacci is a mathematical sequence where you take the last two terms of the sequence and add them together in order to get the next number in the sequence. Fibonacci sequences and patterns can be found in nature.
Fibonacci in Nature
Fibonacci Fun
Antonia Gasparro
Andrea Zevallos

May 13, 2015

The Fibonacci Sequence
0,1,1,2,3,5,8,13,21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4180, 6765, 10945, 17710, 28655, 46365, 75020, 121385, ...
Phi is the 21st letter in the Greek alphabet. In the Fibonacci sequence it represents the number 1.618. Phi is considered an unusual number in the Fibonacci code. If Phi is multiplied by itself, it results in a number exactly 1 greater then 1.618. If Phi is divided by 1 the result will be a number that is exactly 1 less than the original number.
Random Facts
Before the Fibonacci sequence was discovered in Europe, it was used in India for prosody, the study of poetic meter.
Leonardo Fibonacci originally used it to represent rabbit population growth. This has also been applied to cow population and honey bee populations.
Fibonacci numbers are often called pine cone numbers due to their application to the structure of pine cones.
If you were to construct a group of rectangles in the form of a spiral using Fibonacci numbers as unit lengths, the result bares a resemblance to spirals found on snails, nautilus, and other shells.
This sequence has been used in art because it is considered to create appealing images. One artist and mathematician that used this sequence was Leonardo da Vinci.
The sequence can also be seen in music, particularly by Mozart.
Two consecutive Fibonacci numbers can be seen in tree branches, the amount of leaves on a stem, the structure of pineapples and artichokes, etc.
The human ear is an example of the shape of the Fibonacci spiral.
A piano keyboard has 8 white keys, 5 black keys in groups of 2 or 3. The 14 keys form an octave.
How is Phi determined?
To determine Phi:
-A) Divide 1 by your number
-B) Add 1
-C) That is your new number, begin again at A

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