The Golden Ratio is Real!
July 07, 2021

Have you ever thought about the patterns observed in nature? If you carefully notice, the number of petals in any flower, the number of fingers we have, or even the arrangement of the sunflower seeds, all follow a certain pattern. There is a unique ratio that can be used to describe the proportions we see therein. This ratio is known as the "golden ratio." The golden ratio is best approximated by the famous Fibonacci sequence. Let’s find out more about it!

Zoom in shot of a sunflower
Photo by Flash Dantz from Pexels

What is the Fibonacci sequence?

1. History:

Fibonacci numbers are named after the Italian mathematician Leonardo of Pisa, later known as Fibonacci. In his book Liber Abaci, Fibonacci introduced the sequence to Western European mathematics. However, ancient Sanskrit texts that used the Hindu-Arabic numeral system, prove that it was known much before that.

2. The Mathematics:

In mathematics, the Fibonacci numbers commonly denoted Fn, form a never-ending sequence, called the Fibonacci sequence. In the sequence, each number is simply the sum of the two preceding numbers, starting from 0 and 1. 

The Fibonacci sequence is:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

the 2 is obtained by adding the two preceding numbers (1+1),
the 3 is obtained by adding the two preceding numbers (1+2),
the 5 is obtained by adding the two preceding numbers (2+3), and so on!

More than the sequence, what is important is the ratio of the adjacent numbers which consistently comes out to be ~1.618 and it is represented by the Greek letter phi, Φ.

3. The golden ratio in nature:

The golden ratio is also sometimes known as the divine proportion because it is commonly found in so many things in nature. Common examples are the branching of trees, arrangement of leaves on a stem, the number of petals on a flower, the fruitlets of a pineapple, the seeds of sunflowers, the human ear and the family tree of honeybees.

Image by Hans Braxmeier from Pixabay 

4. The golden ratio in architecture:

Ancient Greek architecture is known to use the golden ratio to make their building designs pleasing to the eye. It was achieved by having the dimensions in such a way that the width and the height of the building or the structures had the golden ratio relating them. To quote some more examples, the Great Pyramid of Egypt, the Parthenon in Greece, the Notre Dam in France and the Taj Mahal in India are also structures that have been found to use the golden ratio. However, it cannot be proven that they were intended to be built that way.

Taj Mahal
Image by يسرا توكل from Pixabay 

The golden ratio is just one of the many interesting concepts we have in maths.
Would you like to further explore the world of maths and science? Stay tuned for our next blog.

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