What is the relationship between golden ratio and fibonacci sequence?
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The golden ratio is the limit of theratios of successive terms of theFibonacci sequence (or any Fibonacci-like sequence), as originally shown by Kepler: Therefore, if a Fibonaccinumber is divided by its immediate predecessor in the sequence, the quotient approximates φ; e.g., 987/610 ≈ 1.6180327868852.
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There is a special relationship between the Golden Ratio and Fibonacci Numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, ... etc, each number is the sum of the two numbers before it). So, just like we naturally get seven arms when we use 0.142857 (1/7), we tend to get Fibonacci Numbers when we use the Golden Ratio.
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