The Fibonacci sequence is not so much used as that it appears in thousands of places in the natural world.
However the Fibonacci numbers and principle is also used in the financial markets. It is used in trading algorithms, applications and strategies.
"The bee ancestry code
Fibonacci numbers also appear in the description of the reproduction of a population of idealized bees, according to the following rules:
* If an egg is laid by an unmated female, it hatches a male.
* If, however, an egg was fertilized by a male, it hatches a female.
Thus, a male bee will always have one parent, and a female bee will have two.
If one traces the ancestry of any male bee (1 bee), he has 1 female parent (1 bee). This female had 2 parents, a male and a female (2 bees). The female had two parents, a male and a female, and the male had one female (3 bees). Those two females each had two parents, and the male had one (5 bees). This sequence of numbers of parents is the Fibonacci sequence.[" (Wikipedia)
They are also used in music. they occur on the leaves of sunflowers, and many others.
It is also relevant to the leaf growth on certain plants. That means that the first year those plants grow one new leaf, the second year they grow one new leaf, the third year they grow two new leaves, the fourth year they grow three new leaves, the fifth year they grow five new leaves, the sixth year they grow eight new leaves, and so on..... The pattern 1,1,2,3,5,8,13...is the Fibonacci sequence.
In right triangles, for all triangles with integer sides, (3, 4, 5), (5,12 ,13) and so on have a Fibonacci Number as the hypotenuse.
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