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As you expand the Fibonacci series, each new value in proportion to the previous approaches the Golden Ratio.

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โˆ™ 2010-01-09 18:46:15
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Q: What is golden ratio in Fibonacci series?
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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 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


Is the Fibonacci sequence the golden ratio?

No, but the ratio of each term in the Fibonacci sequence to its predecessor converges to the Golden Ratio.


How is the golden ratio devised?

The 'golden ratio' is the limit of the ratio of two consecutive terms of the Fibonacci series, as the series becomes very long. Actually, the series converges very quickly ... after only 10 terms, the ratio of consecutive terms is already within 0.03% of the golden ratio.


How does the golden ratio relate to the Fibonacci sequence?

The golden ratio is approximately 1.618: 1. This ratio is commonly found in nature and architecture. Stock traders often look for this ratio in patterns on stock charts. One way to compute this ratio is to compare any adjacent Fibonacci numbers. For this reason stock traders often refer to this type of analysis using the term Fibonacci, as in "Fibonacci retracements".


How can a golden ratio be measured?

with a Fibonacci gauge


When and how is the Fibonacci Sequence used?

The Fibonacci sequence can be used to give ever increasing accurate approximations of phi, the golden ratio, by dividing a number in the series by the one before it.


How does the golden ratio apply to the Fibonacci sequence?

As you carry out the Fibonacci Series to more terms, the ratio between two consecutiveterms gets closer to the Golden Ratio.The Fibonacci Series 'converges' exceptionally quickly. That means that you don't need tocarry it very far in order to get as close to the Golden Ratio as you really need to be forany practical purpose.But if you're trying to find the number for the Golden Ratio, the Fibonacci Series is not theeasiest way to get it.An easier way is to just use a calculator, and evaluate 0.5 [ 1 + sqrt(5) ] .That's the solution tox - 1 = 1/xwhich is a pretty good definition for the Golden Ratio . . . "The number that's 1 more than its reciprocal".


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 ].


How are pentagrams related to Fibonacci numbers?

The pentagram is related to the golden ratio, because the diagonals of a pentagram sections each other in the golden ratio. The Fibonacci numbers are also related to the golden ratio. Take two following Fibonacci numbers and divide them. So you have 2:1, 3:2, 5:3, 8:5 and so on. This sequence is going to the golden ratio


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.


What is the limit of the ratio of consecutive terms of the Fibonacci sequence?

The limit of the ratio is the Golden ratio, or [1 + sqrt(5)]/2

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