Golden Ratio to find Fibonacci Sequence
The golden ratio is a ratio between two numbers that is approximately 1.618. It is represented by the Greek letter phi “Φ”, and is also known as the golden number, golden proportion, or the divine proportion. We have observed that by taking the ratio of two consecutive terms of the Fibonacci Sequence we get the ratio called the “Golden Ratio“.
Φ = Fn/Fn-1
Golden Ratio Formula
The golden ratio is derived by dividing each number of the Fibonacci series by its immediate predecessor. The formula for the golden ratio is ϕ = 1 + (1/ϕ).
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The ratio of these two terms are,
F11/F10 = 89/55 = 1.618 (Golden Ratio)
Here the ratio so obtained is called the golden ratio. {Φ = 1.618 (Golden Ratio)}
We can also calculate the Fibonacci number using the golden ratio by the formula:
Fn = (Φn – (1-Φ)n)/√5
where, Φ is the Golden ratio.
Check: Fibonacci Series
Fibonacci Sequence: Definition, Formula, List and Examples
Fibonacci sequence is a series of numbers where each number is the sum of the two numbers that come before it. The numbers in the Fibonacci sequence are known as Fibonacci numbers and are usually represented by the symbol Fₙ. Fibonacci sequence numbers start with the following 14 integers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233.
Table of Content
- Fibonacci Sequence
- Fibonacci Sequence Formula
- Fibonacci Spiral
- Golden Ratio to find Fibonacci Sequence
- Golden Ratio Formula
- Fibonacci Series in Pascal’s Triangle
- Fibonacci Sequence Properties
- Fibonacci Sequence Examples
- Practice Problems on Fibonacci Sequence
- Fibonacci Sequence – FAQs
There are various applications of Fibonacci sequence in real life, such as in the growth of trees. As the tree grows, the trunk grows and spirals outward. The branches also follow the Fibonacci sequence, starting with one trunk that splits into two, then one of those branches splits into two, and so on.
Let’s learn about Fibonacci Sequence in detail, including Fibonacci sequence formula, properties, and examples.