Transcript Fibonacci Number Powerpoint

http://www.youtube.com/watch?v=kkGeOWYOFoA
Original Question:
How fast rabbits can rabbits breed
in ideal circumstances?
Suppose a newly-born pair of
rabbits, one male, one female, are
put in a field. Rabbits are able to
mate at the age of one month so
that at the end of its second month
a female can produce another pair
of rabbits.
Suppose that our rabbits never die
and that the female always
produces one new pair (one male,
one female) every month from the
second month on. The puzzle that
Fibonacci posed was...
How many pairs will there be in one
year?
Each number created by adding the two previous numbers
1,
1,
2,
3,
5,
8,
13,
21,
…
What are the next 5
Fibonacci numbers?
34, 55, 89, 144, 233, …
This sequence has
fascinated
mathematicians for
centuries…
Flower Petals:
MOST flowers have petals that
occur in Fibonacci numbers
(1, 2, 3, 5, 8, …)
Very few flowers have petals
that do not occur in Fibonacci
numbers (4, 6, 7, …)
3 petal
13 petal
21 petal
Not to mention, we
have 2 hands,
each with 5 fingers,
each with 3 parts!
A
Fibonacci Rectangle (the Golden
Rectangle) is created by taking the
Fibonacci numbers and arranging them
as shown:
 By
drawing the curve through the corners
of the boxes, we create something called
the golden spiral (or sometimes
logarithmic spiral)
The most classic example of
the golden spiral in nature is
the cross section of the
chambers of the Nautilus
Shell.
If you start dividing the Fibonacci numbers
backwards, the quotient gets closer and
closer to the number 1.618
2/1=2
3/2=1.5
5/3=1.667
8/5=1.6
13/8=1.625
21/13=1.615
34/21=1.619
55/34=1.618
89/55=1.618
144/89=1.618
We call this number φ
It can be pronounced
“Fee” or “Fye”
Φ=1.618… and is called
the Golden Ratio
 The
golden ratio is
considered to be the most
aesthetically pleasing ratio
to the human eye. It is
used in art, architecture,
and advertising.
 Any
rectangle whose length
÷ width ≈ 1.618 is called a
golden rectangle.
Apple IPOD dimensions
are 1:1.67 and is the
closest MP3 player to the
golden ratio.
Some people are obsessed with
finding golden ratios in
everything they see. The see
the shape of cereal boxes,
cigarette packages, and notecards as a giant
conspiracy.
Jack Ruby shoots assassin Lee Harvey Oswald in this famous news photo.
The area taken up by Ruby: the area taken up by Oswald = 1.618
There are just as many sources that say
that finding Fibonacci and the Golden
Ratio “EVERYWHERE” is garbage.
Google “Fibonacci Skeptics” to find much
discourse on the subject.

You may see
Fibonacci
numbers written
as Fn
F1 = 1
F2 = 1
F3 = 2
F4 = 3
F5 = 5
F6 = 8
etc…
What is F10?
55
Recursive Definition of
Fibonacci Numbers:
FN = FN-1 + FN-2
Euler improved
another
mathematician’s
theorem to show
that:
10
 1 5   1 5 

 

2   2 

F10 
5
1.618


  .618
2.236
10
F10
10
10
122.966  .008
F10 
2.236
F10  54.990
Not a bad estimate for 55!
You don’t have to know the 8th and
9th Fibonacci numbers to find it!
http://www.youtube.com/watch?v=kkGeOWYOFoA