Golden Ratio
Ratio of two consecutive numbers is called Golden Ratio. It is denoted by “φ“. The golden ratio is generally seen in nature, and when applied in a design, it fosters natural-seeming works that are pleasing to the eye. There are numerous operations of the golden ratio in the field of architecture. For illustration, the Great Pyramid of Egypt and the Great Mosque of Kairouan is many of the architectural miracles in which the notion of the golden ratio has been applied.
For example:
| X | Y | Y/X |
|---|---|---|
| 2 | 3 | 1.5 |
| 3 | 5 | 1.6666 |
| 5 | 8 | 1.6 |
| 8 | 13 | 1.625 |
| 13 | 21 | 1.6154 |
| 21 | 34 | 1.6190 |
| 34 | 55 | 1.6176 |
| 55 | 89 | 1.6181 |
| 89 | 144 | 1.6179 |
Note: Golden Ratio can be calculated from Any Fibonacci sequence, it does not necessarily have to start with 2 and 3.
Fibonacci Sequence Formula
Fibonacci Sequence Formula: Fibonacci sequence, the sequence of numbers 1, 1, 2, 3, 5, 8, 13, 21, …, each of which, after the second, is the sum of the two previous numbers; that is, the nth Fibonacci number Fn = Fn − 1 + Fn − 2.
In the Fibonacci sequence, each number in the series is calculated by adding the two numbers before it. Generally, the first two terms of the Fibonacci series are 0 and 1. The Fibonacci sequence was known in India hundreds of years before Leonardo Pisano Bigollo knew about it. November 23rd is celebrated as Fibonacci Day, as it has the digits “1, 1, 2, 3” which is part of the sequence
In this article, we will learn about the Fibonacci Sequence, along with its formula, examples, golden ratio, etc.
Fibonacci Sequence Formula
Table of Content
- What is the Fibonacci Sequence?
- Fibonacci Sequence Formula
- Golden Ratio
- Calculating the Fibonacci sequence
- Fibonacci Sequence Examples
- Practice Problems on Fibonacci Sequence Formula