Fibonacci Forever

Some interesting facts about a famous sequence

1,1,2,3,5,8,13,21,34,55,89...

Generated by An = An-1 + An-2

Pascal's triangle contains fibonacci sequence

Fibonacci and Nature

Picture of 3 petal flowers Picture of banana cross section

3 petaled flowers include:
Trillium, Iris, Lilies...,
Banana cross-section

Picture of 5 petal flowers

5 petaled flowers include:
Columbine, Buttercup, Roses ...

Picture of 8 petal flowers Picture of 8 petal flowers

8 petaled flowers include:
Rose, Bloodroot, Delphinium

Picture of 13 petal flowers

13 petaled flowers include:
Black-eyed Susan

Picture of 21 petal flowers

21 petaled flowers include:
Shasta Daisy, Aster, Chicory

Picture of 34 petal flowers

34, 55, 89 petaled flowers include:
Field daisy, Plaintain, Pyrethrum

Picture of pineapple Picture of pineapple

Spirals in pineapples
(5 shallow, 8 steep spirals)

Picture of branching

Number of branches at each level

Picture of fibonacci ratios

Ratio of successive fibonacci numbers:

1/1 = 1,
2/1 = 2,
3/2 = 1·5,
5/3 = 1·666...
8/5 = 1·6,
13/8 = 1·625,
21/13 = 1·61538...

References:

britton.disted.camosun.bc.ca/fibslide/jbfibslide.htm
goldennumber.net/plants.htm
goldennumber.net/pascal.htm