Introduction

Have you ever wondered how some things look incredibly attractive to you in a way you don’t understand? Ever wondered why these things make you feel satisfied or pleased whether it's an object or a human’s face? Well, as surprising as it may sound, this ‘attraction’ you have towards something involves a mathematical explanation.

The Golden Ratio, also known as ‘The Golden Mean’, ‘The Golden Section’, ‘Divine Proportion’, is a ratio of the two sections, that is defined as the perfect illustration of beauty. It is an irrational number—which goes on forever—approximately equal to 1.68, that can also be described with the symbols ϕ or τ.

Origin

The golden ratio was first exposed in ‘The Elements of Euclid’, a book by the Greek mathematician, Euclid. It was discovered by dividing a line into two parts such that the long part divided by the short part is equal to the whole part divided by the long part. The result of the numbers also follows the Fibonacci sequence.

The ratio of each number to the previous number in the Fibonacci sequence is equal to phi’ (=1.618…). When you draw a rectangle and divide it by the aforementioned ratio, you get the golden ratio. The ratio was first named ‘Golden’ by a German mathematician, Martin Ohm in his book ‘Die Reine Elementar-Mathematik’ (The Pure Elementary Mathematics) in 1815, where he used ‘goldener schnitt’, referring to the golden section.

The golden ratio was believed to influence many ancient Greece architecture for its aesthetic properties. Additionally, the golden ratio can be seen in many iconic works of art from the ancient renaissance and music pieces.

Golden Ratio in Nature

Did you know that the golden ratio is also a part of the human body structure? Although the appearance of humans can vary for every single person the ratio of some structures is the same. For example, the human skull dimension, the sizes of your canines and incisors, your palm and finger, etc.

Not only in humans but the golden ratio can also be found in almost every part of nature.

• The lily has 3 petals, buttercups have five, chicory 21 and so on. Do you notice the Fibonacci sequence here? Let’s find another example.

• Snail shells and nautilus shells follow the golden ratio, drawn in sections of a circle.

• The animal bodies also contain the ratio as well. The ratio of the distance between the navel to the floor and the distance between the top of the head and the navel is also the golden ratio.

Although some people believe the discovery of the golden ratio in nature is exaggerated, some still believe this ratio is an astonishing phenomenon and can be used to complete theories in many fields.

Is it still used in modern life?

It is still a debate whether modern designs and artworks use the golden ratio since the works by artists and designers are highly confidential and secured.

[1] G. Meisner, “History of the Golden Ratio”, May 2012. [Online] Available: https://www.goldennumber.net/golden-ratio-history/ [Accessed 18 August 2022] [2] S. C. Carlson, “golden ratio”, August 2022. [Online] Available: https://www.britannica.com/science/golden-ratio [Accessed 18 August 2022] [3] G. Dvorsky, “14 INTERESTING EXAMPLES OF THE GOLDEN RATIO IN NATURE”, April 2017.[Online] Available:https://www.mathnasium.com/blog/14-interesting-examples-of-the-golden-ratio-in-nature [Accessed 18 August 2022]