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Fibinochi number system

KenH

Well-Known Member
"The Fibonacci sequence is a set of numbers that starts with a one or a zero, followed by a one, and proceeds based on the rule that each number (called a Fibonacci number) is equal to the sum of the preceding two numbers. If the Fibonacci sequence is denoted F (n), where n is the first term in the sequence, the following equation obtains for n = 0, where the first two terms are defined as 0 and 1 by convention:

F (0) = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ...

In some texts, it is customary to use n = 1. In that case, the first two terms are defined as 1 and 1 by default, and therefore:

F (1) = 1, 1, 2, 3, 5, 8, 13, 21, 34 ...

The Fibonacci sequence is named for Leonardo Pisano (also known as Leonardo Pisano or Fibonacci), an Italian mathematician who lived from 1170 - 1250. Fibonacci used the arithmetic series to illustrate a problem based on a pair of breeding rabbits:

"How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on?" The result can be expressed numerically as: 1, 1, 2, 3, 5, 8, 13, 21, 34 ...

Fibonacci numbers are of interest to biologists and physicists because they are frequently observed in various natural objects and phenomena. The branching patterns in trees and leaves, for example, and the distribution of seeds in a raspberry are based on Fibonacci numbers"

What is Fibonacci sequence? - Definition from WhatIs.com (techtarget.com)
 

37818

Well-Known Member
Can anyone explain in very simple terms
the purpose of Fibonacci number - Wikipedia
It is a natural occuring number set. It defines all kinds of things we see in nature. The golden ratio from it defines what we perceive as beauty. 1.618. . . / 1 = 1 / 0.618 . . .
0 1 1 2 3 5 8 13 21 34 55 . . .

The ratio of the sequence 55/34 = 1.61764 . . .
The ratio apporches the limit which is the Fibonacci number, 1.618033988 . . . .
1.6180 . . . = (sqr (5) + 1) / 2

I hope this helps. It is one of many important constants in our universe.

Golden ratio - Wikipedia

https://www.google.com/search?q=images+of+the+golden+ratio+as+seen+in+nature.
 
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Alcott

Well-Known Member
Site Supporter
It can be seen on a piano keyboard, with those black keys and white keys. Begin with the middle C, then in an octave, you see 2 black keys, separated by one white, then 3 black keys separated by 2 whites, 5 black keys altogether (in the octave), and 8 white keys, making up 13.

So you 1, 2, 3, 5, 8, and 13.
 
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