The Golden Ratio is Real!

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.

The proportions we see therein can be described using a unique ratio known as the “golden ratio.” The famous Fibonacci sequence approximates the golden ratio. 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. The history:

The Italian mathematician Leonardo of Pisa, later known as Fibonacci, gives his name to the Fibonacci numbers. 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, …

Adding the two preceding numbers (1+1) gives us 2, (1+2) gives us 3, (2+3) gives us 5, and so on. The ratio of the adjacent numbers consistently comes out to be ~1.618, 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.

Sun rays falling on a cauliflower in a field
Image by Hans Braxmeier from Pixabay 

4. The golden ratio in architecture:

Ancient Greek architecture used the golden ratio to create pleasing building designs. The dimensions of the buildings or structures related the width and height using the golden ratio.

To quote some more examples, the Great Pyramid of Egypt, the Parthenon in Greece, the Notre Dame 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.