The History of the Golden Ratio and its uses

Read this article to learn about how the golden ratio helps us understand the world on a deeper level and its history.

Have you ever wondered why the petals of flowers are beautiful and snail shells look pretty? Have you ever thought about why human faces seem very attractive? Well, your attraction towards something involves a mathematical explanation called the ‘Golden Ratio’.

What is Golden Ratio?

The golden ratio, also known as the golden section or divine proportion is the ratio between two sections approximately equal to 1.618. It is also denoted by the Greek letter ‘phi’ ϕ. The golden ratio is strongly associated with the Fibonacci sequence, a series of numbers wherein each number is added to the last. The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. The ratio of each number and the previous number in the sequence gradually approaches 1.618.

We can also use the Fibonacci sequence to construct the Fibonacci spiral.

Figure 1 & 2: Fibonacci spiral

The history of the Golden Ratio

It appears that the Egyptians used the Golden Ratio in the design of pyramids. However, 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. At this time, mathematicians did not call it 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.

Examples of the golden ratio

Many painters and artists used the Golden Ratio in their artistic masterpieces in the ancient era. They used the ratio to add beauty and make their art in perfect proportion. Leonardo da Vinci’s famous painting, the Mona Lisa, is based on the Golden Ratio and is considered the most beautiful painting having perfect facial proportions.

Figure 3: Mona Lisa painting

The golden ratio can also be found in nature.

1. Faces

The structure of human faces is strongly associated with the golden ratio. A visually balanced face is approximately 1.618 times longer than it is wide. The more it is closer to 1.618, the more beautiful the face is according to the beauty standards. We also have to measure the position of the eyes, ears, nose and lips to find a perfect facial structure.

2. Petals

The number of petals in a flower consistently follows the Fibonacci sequence.8 petal rose has one petal in its centre, 3 petals around that, then five around that.

3. The Milky Way galaxy and the shell of the snail

The shape of the Milky Way galaxy and the shell of the snail also follow the structure of the Fibonacci spiral.

The golden ratio is still used in the modern world by architects and graphic designers to achieve a range of aesthetics.