math – update

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Day # 13: Fibonacci Numbers – From 0 and 1 to Unbounded Imagination

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0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …
Animated GIF showing successive tilings with squares whose side lengths are successive Fibonacci numbers  +  a graph of approximations to the Golden Ratio calculated by the sequence of ratios   1/1, 2/1, 3/2, 5/3, 8/5, 13/8, ……. , 89/55, 144/89   given by pairs of consecutive Fibonacci numbers.

Johannes Kepler observed that the ratio of consecutive Fibonacci numbers converges. He wrote that “as 5 is to 8 so is 8 to 13, practically, and as 8 is to 13, so is 13 to 21 almost”, and concluded that the limit approaches the golden ratio \varphi .[25][26]

X-MATHS Rabbits´ Population Growth and the

Fibonacci Sequence

II

Recent history studies have shown that the most probable inspiration for this extraordinary sequence was not exactly rabbits but something else… Cold you tell what??…

A: The Bee Ancestry Code

Fibonacci numbers also appear in the pedigrees of idealized honeybees, according to the following rules:

  • If an egg is laid by an unmated female, it hatches a male or drone bee.
  • If, however, an egg was fertilized by a male, it hatches a female.

Thus, a male bee always has one parent, and a female bee has two.

If one traces the pedigree of any male bee (1 bee), he has 1 parent (1 bee), 2 grandparents, 3 great-grandparents, 5 great-great-grandparents, and so on. This sequence of numbers of parents is the Fibonacci sequence. The number of ancestors at each level, Fn, is the number of female ancestors, which is Fn−1, plus the number of male ancestors, which is Fn−2.[65] This is under the unrealistic assumption that the ancestors at each level are otherwise unrelated.

Source: WikipadiA

 

 

 

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Author: Math - Update

Updating Math In Our Mind & Heart!!...

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