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# What are the relations between the golden ratio and the Fibonacci series?

Updated: 12/20/2022

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12y ago

The ratio of successive terms in the Fibonacci sequence approaches the Golden ratio as the number of terms increases.

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12y ago

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Q: What are the relations between the golden ratio and the Fibonacci series?
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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 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 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".

### Is 20 a Fibonacci number?

20 is not a term in the Fibonacci series.

### What is the next in this sequence 112358?

There are many possible answers. One obvious one is 13, the next number in the Fibonacci Sequence that yields the golden mean.

### When and how is the Fibonacci Sequence used?

The Fibonacci sequence is used for many calculations in regards to nature. The Fibonacci sequence can help you determine the growth of buds on trees or the growth rate of a starfish.

### 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 ].

Fibonacci!

### 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.

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