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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 the
most perfect and visually pleasing ratio of structural length to width. Fibonacci studied a
simple numerical series that generates the number equal to the golden ratio.
The number is also the solution to the equation: [ (x - 1) = 1/x ].
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What are the relations between the golden ratio and the Fibonacci series?
The ratio of successive terms in the Fibonacci sequence approaches the Golden ratio as the number of terms increases.
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
A side of math where can you find the golden ratio?
The Fibonacci sequence can be used to determine the golden ratio. If you divide a term in the sequence by its predecessor, at suitably high values, it approaches the golden ratio.
How is Lenardo Fibonacci discoverey used in science?
Your mind will be blown if you search Phi, The golden ratio, or the fibonacci sequence. It has to do with everything.
