Where is fibonacci series used

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Develop and improve products. List of Partners vendors. Fibonacci numbers are used to create technical indicators using a mathematical sequence developed by the Italian mathematician, commonly referred to as "Fibonacci," in the 13th century.

The sequence of numbers, starting with zero and one, is created by adding the previous two numbers. For example, the early part of the sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,, , , and so on. This sequence can then be broken down into ratios which some believe provide clues as to where a given financial market will move to.

The Fibonacci sequence is significant because of the so-called golden ratio of 1. In the Fibonacci sequence, any given number is approximately 1. Each number is also 0. The golden ratio is ubiquitous in nature where it describes everything from the number of veins in a leaf to the magnetic resonance of spins in cobalt niobate crystals. Fibonacci numbers don't have a specific formula, rather it is a number sequence where the numbers tend to have certain relationships with each other.

The Fibonacci number sequence can be used in different ways to get Fibonacci retracement levels or Fibonacci extension levels. Here's how to find them. How to use them is discussed in the next section. Fibonacci retracements require two price points to be chosen on a chart, usually a swing high and a swing low. Fibonacci extension levels are also derived from the number sequence. As the sequence gets going, divide one number by the prior number to get a ratio of 1. Divide a number by two places to the left and the ratio is 2.

Divide a number by three to the left and the ratio is 4. A Fibonacci extension requires three price points. Fibonacci was not the first to know about the sequence, it was known in India hundreds of years before! That has saved us all a lot of trouble!

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August 7, So, one amoebas becomes two, two become 4, then 8, 16, 32, and so on. We get a doubling sequence. Now in the Fibonacci rabbit situation, there is a lag factor; each pair requires some time to mature. The number of such baby pairs matches the total number of pairs in the previous generation. So we have a recursive formula where each generation is defined in terms of the previous two generations. Using this approach, we can successively calculate fn for as many generations as we like.

So this sequence of numbers 1,1,2,3,5,8,13,21, But what Fibonacci could not have foreseen was the myriad of applications that these numbers and this method would eventually have. His idea was more fertile than his rabbits. Just in terms of pure mathematics - number theory, geometry and so on - the scope of his idea was so great that an entire professional journal has been devoted to it - the Fibonacci Quarterly.

Now let's look at another reasonably natural situation where the same sequence "mysteriously" pops up. Go back years to 17th century France. Blaise Pascal is a young Frenchman, scholar who is torn between his enjoyment of geometry and mathematics and his love for religion and theology. The Chevalier asks Pascal some questions about plays at dice and cards, and about the proper division of the stakes in an unfinished game. Pascal's response is to invent an entirely new branch of mathematics, the theory of probability.

This theory has grown over the years into a vital 20th century tool for science and social science. Pascal's work leans heavily on a collection of numbers now called Pascal's Triangle , and represented like this: This configuration has many interesting and important properties: Notice the left-right symmetry - it is its own mirror image.

Notice that in each row, the second number counts the row. There are endless variations on this theme. Next, notice what happens when we add up the numbers in each row - we get our doubling sequence.

Now for visual convenience draw the triangle left-justified. Add up the numbers on the various diagonals Fibonacci could not have known about this connection between his rabbits and probability theory - the theory didn't exist until years later.

What is really interesting about the Fibonacci sequence is that its pattern of growth in some mysterious way matches the forces controlling growth in a large variety of natural dynamical systems. Quite analogous to the reproduction of rabbits, let us consider the family tree of a bee - so we look at ancestors rather than descendants.