Fibonacci

The Fibonacci sequence is a series of numbers which are commonly found in nature and lead to such mathematical and artistic concepts as the Golden Ratio.

The sequence is as follows:

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

Fn = Fn-1 + Fn-2

A Fibonacci number is the sum of the previous two numbers in the sequence.

Fibonacci numbers appear frequently in nature. The number of spirals on a fur cone, the number of petals on a flower.

By constructing a series of boxes, starting with unit side one, and then increasing the size through the Fibonacci series, it is possible to simulate the cross section of a spiral shell. Each box in the sequence contains a one-quarter circle which is joined to the next box. The resulting pattern exactly follows the spiral which grows naturally in a shell.

The ratio of any two consecutive numbers in the Fibonacci series approximates to the Golden Ratio.

2 divided by 1 = 2.0000000000
3 divided by 2 = 1.5000000000
5 divided by 3 = 1.6666666667
8 divided by 5 = 1.6000000000
13 divided by 8 = 1.6250000000
21 divided by 13 = 1.6153846154
34 divided by 21 = 1.6190476190
55 divided by 34 = 1.6176470588
89 divided by 55 = 1.6181818182
144 divided by 89 = 1.6179775281
233 divided by 144 = 1.6180555556
377 divided by 233 = 1.6180257511
610 divided by 377 = 1.6180371353
987 divided by 610 = 1.6180327869
1597 divided by 987 = 1.6180344478
2584 divided by 1597 = 1.6180338134

Golden Ratio = 1.6180339887……