F I B O N A C C IS QE ECNEU

A Little Bit of History….• The Fibonacci sequence is

named after Leonardo of Pisa who was known as Fibonacci. Fibonacci's 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been described earlier in Indian mathematics.

The Fibonacci Sequence is a group of numbers which starts with the numbers 0 and 1, and each subsequent Fibonacci number is the sum of the previous 2. 0 21

1 35

813

Here is a Longer List ….. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811

In mathematical terms the Fibonacci sequence is defined by the following relation

Fn=Fn-1+Fn-2 * Where n is equal to the

number of that term in the sequence.

Painting by NumbersThe Fibonacci Sequence in Art

The Fibonacci sequence has one very special property. If you take the fourth Fibonacci number, 3, and divide it by the third, so 3 divided by 2 it gives you about 1.67. If you keep trying this with higher and higher Fibonacci numbers, you’ll see that your answers get closer and closer to a certain number. This number, approximately equal to 1.618034, is known as the golden ratio, the golden mean, and even the divine ratio and is a very special value

The Golden Ratio

As the Fibonacci Sequence is closely related to the Golden Ratio it is found in famous works of art. It is considered a naturally elegant number sequence and using it is said to create very aesthetically pleasing images. The Mona Lisa:

Leonardo Da Vinci’s famous portrait of a mysterious woman incorporates the Fibonacci sequence into its design in a very subtle way. As you can see highlighted in the image to the left, the woman’s figure traces out the ratio between the Fibonacci numbers.

Almost everything has dimensional properties that adhere to the ratio of the Fibonacci Sequence 1.618 , so it seems to have a fundamental function for the building blocks of nature. For example honeybees. If you divide the female bees by the male bees in any given hive, you will get 1.618. Sunflowers, which have opposing spirals of seeds, have a 1.618 ratio between the diameters of each rotation. This ratio is even seen in the human body, measuring from your shoulder to your fingertips, and then divide this number by the length from your elbow to your fingertips and you are left with the Fibonacci Sequence.

Why does it matter?