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What is golden ratio in Fibonacci series?
As you expand the Fibonacci series, each new value in proportion to the previous approaches the Golden Ratio.
What is the relationship between the golden ratio and the standard Fibonacci sequence?
The "golden ratio" is the limit of the ratio between consecutive terms of the Fibonacci series. That means that when you take two consecutive terms out of your Fibonacci series and divide them, the quotient is near the golden ratio, and the longer the piece of the Fibonacci series is that you use, the nearer the quotient is. The Fibonacci series has the property that it converges quickly, so even if you only look at the quotient of, say, the 9th and 10th terms, you're already going to be darn close. The exact value of the golden ratio is [1 + sqrt(5)]/2
How did Fibonacci discover the golden ratio?
Fibonacci didn't discover the golden ratio. It had been used thousands of years earlier,for example in construction of religious architecture by the Greeks, who considered it themost perfect and visually pleasing ratio of structural length to width. Fibonacci studied asimple numerical series that generates the number equal to the golden ratio.The number is also the solution to the equation: [ (x - 1) = 1/x ].
For what purpose Fibonacci sequence numbers are used?
The Fibonacci sequence is a series of numbers in which each number is the sum of the two previous numbers. When graphed, the sequence creates a spiral. The sequence is also related to the "Golden Ratio." The Golden Ratio has been used to explain why certain shapes are more aesthetically pleasing than others.
What is Fibonacci number series?
A Fibonacci number series is like the example below, 1,1,2,3,5,8,13,21,34,55,89,144,233,377,610...... and so on in general Fibonacci numbers are just the previous two numbers added together starting with 1 and 0 then goes on forever.
