How does the golden ratio relate to the Fibonacci sequence?

Ignacio Riggs

Ignacio Riggs

Answered question

2022-10-21

How does the golden ratio relate to the Fibonacci sequence?

Answer & Explanation

Amadek6

Amadek6

Beginner2022-10-22Added 21 answers

Explanation:
If you take two consecutive terms in the Fibonacci Sequence, or indeed any given sequence, and divide one of the terms by the one that comes before it, then you get a number that will get closer and closer to ϕ , or 1.618033988...
An example is the division 34 ÷ 21 , which gives the answer 1.61904762. Going even further to 17711 ÷ 10946 , which gives 1.61803399.
In addition, there is a direct formula for F n in terms of ϕ :
F n = ϕ n - ( - ϕ ) - n 5

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