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Fibonacci: The Beauty that is Hidden

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by

Angel Bassig

on 7 September 2013

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Transcript of Fibonacci: The Beauty that is Hidden

Fibonacci: The Beauty that is Hidden
Fibonacci: The Beauty that is Hidden
MATHEMATICS
Fibonacci Numbers
nature
architecture
painting
sculpture
music
finance

Fibonacci: The Beauty that is Hidden
Fibonacci numbers in nature
Fibonacci numbers & the golden number
Investigation on the existence of the golden number around us
Provides science and technology with its language and power.
It is a way of thinking, a way of looking at and making sense of this world.
Its products and impact are everywhere!
MATHEMATICS
Products of Mathematics
iPhones & iPads
CARS
GPS
sea navigation
study of human vision
3-D screen
. . . and a lot more!!!
PRELIMINARIES
Fibonacci Numbers are popularised in:
“The Da Vinci Code” (BOOK)
“Mr. Magorium’s Wonder Emporium”. (MOVIE)
Leonardo de Pisa
FIBONACCI RABBIT PROBLEM
In his book Liber Abaci, Fibonacci posed and solved a problem involving the reproduction of rabbits.
Fibonacci’s ideal conditions under which rabbits could breed
“How many pairs will there be in one year?”
Liber Abaci
Fibonacci cited through an example what we feature in this paper – the Fibonacci numbers.
Italian born
studied Hindu-Arabic numbers with Arab mathematicians
spread the Hindu-Arabic numeral system in Europe through his book Liber Abaci
greatest Western mathematician of the Middle Ages
Fibonacci in
Nature
Fibonacci Flowers
Fibonacci Spirals
Fibonacci & the Golden Number
White Calla Lily
1 Petal
Trillium
3 Petals
Columbine
5 Petals
Bloodroot
8 Petals
Black-eyed Susan
13 Petals
Fibonacci Flowers
Euphorbia
2 Petals
Fibonacci Flowers
Shasta Daisy
21 Petals
Sunflower
34 Petals
Michaelmas Daisies
55 Petals
1. A newly born pair of rabbits, one male and one female, are put in a closed field.
2. Rabbits are able to mate at the age of one month.
3. Once a female rabbit has started giving birth, it will continue giving birth every month.
4. The pregnancy period of a rabbit is one month so that at the end of its second month a female rabbit can produce another pair of rabbits – one male and one female.
5. A female rabbit will always give birth to one male rabbit and one female rabbit.
6. Rabbits never die.
Conditions by which rabbits could breed
An apple cut along the equator has 5 flat surfaces
A banana cut in half has 3 flat surfaces
Lettuce has 5 leaves that do not overlap
Cauliflower
Pine Cone
Fibonacci Fruits & Vegetables
Brocolli
Golden Number
or
Golden Ratio
Parthenon of the Greeks is influenced by the Golden Number
Pyramids of the Egyptians
Almost anything that seems appealing and attractive to the eye adheres to this number.
The Golden Ratio is approximately equal to 1.6180339887498948482.
Spirals in Nature
(Inspiration Green, n.d.)
is related to the Ficonacci Numbers in a very special way
appearances of the Golden Number
Sea Shells
BUILDINGS
Art works
Flowers
Ferns
Golden Ratio is related to Fibonacci Numbers is 2 WAYS
1. The Golden Number can be obtained easily by getting the ratio of any two consecutive (one after the other) Fibonacci numbers.
2. We can construct a Golden Rectangle - a rectangle that can be cut up into a square and a rectangle similar to the original one - using squares that had successive side lengths from the Fibonacci numbers.
Authors:
Alyazia
Salama
Walla
Ms. Angel
Fibonacci Squares & the Golden Rectangle
Golden Ratio Investigation
Results
Our results show how the Golden Ratio played its role behind the beauty and appearance of the usual things that we see around us.
Conclusion
We know that nature has no prior knowledge and has no understanding of mathematics as we do, yet it performs its own mathematics in an amazing way, helping us – who were endowed by our Creator to grasp and understand – taste, see, enjoy, and benefit from this highly interesting subject.
We hope that this paper will be instrumental indeed in cultivating and enhancing appreciation of this marvelous subject called Mathematics.
THANK YOU!!!
Transmitting communications via phones and computers (satellite communication)
security of computer networks
internet routing protocols and search engines such as Google
This tells us that we live in a world CREATED by
MATHEMATICS
Help cultivate mathematics appreciation among youngsters like us - for whom lie the furtherance and progress of research, through the unveiling of the beauty of the amazing Fibonacci numbers in nature.
GOAL
Fibonacci in Nature
Full transcript