Especially in the world of art, architecture and design, the Golden Ratio is a number used in his work by big names such as Le Corbusier and Salvador Dalí. The Parthenon, the Pyramids of Giza, Michelangelo’s paintings, the Mona Lisa and even Apple’s logo are said to contain the Golden Ratio. Since the Golden Ratio, also called the divine ratio, mathematically indicates an extremely balanced and proportional value (the number of fi), its reflection in objects in nature is thought to evoke aesthetic feelings in our minds. Below, we talked about both the characteristics of the Golden Ratio and its reflections in nature.

## Points of interest for the Golden Ratio

It is irrational, such as the Golden Ratio or the number fi, pi, or E. So it goes on forever without repeating itself. Mathematicians, scientists and naturalists realized the Golden Ratio centuries ago. They denoted it by ϕ or τ. Further popularising the idea that there is a mathematical proportion in nature came from the Italian Leonardo Fibonacci (his birth is assumed to be around 1175 AD and his death around 1250 AD). The name” Golden Ratio ” is derived from the Fibonacci sequence. In a Fibonacci sequence that grows to Infinity, each number is the sum of the previous two numbers: 1, 1, 2, 3, 5, 8, 13, 21… and it goes on.

What makes this order important and valuable is how it grows, that is, the rate of growth. When this ratio is calculated, the value (1 + √5)/2 is 1,618 (or 0.618, which is vice versa). By dividing a number in the array by the number to its left (21/13), you can also reach roughly 1,618. Almost everything in nature has a dimensional ratio of 1,618.

There is a unique value that explains the proportion of the most advanced models in the universe, from the smallest building block such as the Atom to plants and unimaginably large celestial bodies such as giant stars and galaxies in the sky. All the balance in nature is present thanks to this ratio. As many objects in nature grow, such as a flower or snail shell, it does so according to the Golden Ratio and emerges a spiral shape.

It is irrational, such as the Golden Ratio or the number fi, pi, or E. So it goes on forever without repeating itself. Mathematicians, scientists and naturalists realized the Golden Ratio centuries ago. They denoted it by ϕ or τ. Further popularising the idea that there is a mathematical proportion in nature came from the Italian Leonardo Fibonacci (his birth is assumed to be around 1175 AD and his death around 1250 AD). The name” Golden Ratio ” is derived from the Fibonacci sequence. In a Fibonacci sequence that grows to Infinity, each number is the sum of the previous two numbers: 1, 1, 2, 3, 5, 8, 13, 21… and it goes on.

What makes this order important and valuable is how it grows, that is, the rate of growth. When this ratio is calculated, the value (1 + √5)/2 is 1,618 (or 0.618, which is vice versa). By dividing a number in the array by the number to its left (21/13), you can also reach roughly 1,618. Almost everything in nature has a dimensional ratio of 1,618.

## What does it look like?

The easiest way to visualize this ratio is by placing a golden spiral inside the golden rectangle. The golden rectangle is divided into two parts based on the Golden Ratio. As the entire rectangle continues to be divided into small areas with the same ratio, a spiral shape called the golden spiral appears.

## Fibonacci sequence and its relationship with the Golden Ratio

Mathematician Leonardo Fibonacci described the same ratio in 1200 AD in a different way. From his calculations, a magnificent sequence of numbers called the Fibonacci sequence has emerged today. The Fibonacci sequence in which the next number is born by adding the previous two numbers to each other is not exactly the same as the golden ratio, but is extremely close. They are even so close that they are often used as synonyms.

Like the Golden Ratio, Fibonacci numbers start small and gradually grow. In addition, it is impossible to have a final number, since it is irrational, i.e. infinite, such as the Golden Ratio, and does not repeat itself. Below is a rectangle, this time proportional to the Fibonacci numbers. All measurements are quite close.

## Some evidence of the Golden Ratio

For example, when honey bees are considered, dividing the number of female bees in any Hive into male bees always gives the number 1,618.

- In a sunflower whose seeds spread spirally, there is a ratio of 1,618 between the diameter of each turn.
- These same proportions are also seen in the relationship in many other objects in nature.

Those who want to see the golden ratio immediately can take a look at something that can be easily measured: your own body. Measuring from the shoulder to the tip of the finger and then dividing this number by the length from the elbow to the tip of the finger gives the Golden Ratio. Similarly, measuring from head to toe and dividing this by length from belly button to foot gives 1,618. The golden ratio seems inevitable. There are many points where the golden ratio applies, from design to finance.

## History of the Golden Ratio

The history of the Golden Ratio is based on the 12th century AD. – 13. it goes back more than Leonardo Fibonacci, who lived between the centuries. Euclid, who lived in 330 BC – 275 BC, included this number in his book of elements, calling it an “extreme and average ratio”.

More than 2,000 years later, German mathematician Martin Ohm called this ratio “gold” in 1835. Before that, the Greeks discovered that the Golden Ratio provides the most aesthetically pleasing image when applied to the edges of a rectangle. This view began to gain popularity during the Renaissance. The work of the Italian wise Leonardo da Vinci and the publication of the work Divina Proportione (1509; the Divine Oran), written by the Italian mathematician Luca Pacioli and illustrated by Leonardo, led to the development of the idea.

## The golden ratio in nature

Here you are looking at a seashell with a golden ratio. It can also be said that it has a Fibonacci spiral that has the same meaning. The snail shell shows the same ratio. Among other examples, the chameleon’s tail, Fern sprouts, ocean wave, flower, bud, romanesco broccoli, vortex, comfrey flower, pine cone, calla lily, spider, flower petals and more.

In addition to an example of the ratio of female and male bees in the hive, or the angular sequence of sunflower seeds, when you look at spiral galaxies far away, a million light-years away, their geometric shape gives the Golden Ratio.

Even the microscopic world is not separate from the Golden Ratio. Each complete cycle of the double helix spiral in the DNA molecule is 34 angstrom long and 21 angstrom wide. These numbers, i.e. 34 and 21, are found in the Fibonacci series, and their ratio gives 1,6190476, close enough to 1,6180339.

The places where this interesting behavior is easier to see are leaves, branches and flowers. Each grows with a spiral structure corresponding to the ratio below it. The advantage of this is that each new Leaf does not block sunlight from the previous Leaf. At the same time, the maximum rate of rain and dew reaches the roots.

## The Golden Ratio In Math

If the equation (x + 1)/x = x/1, in which the length of the short part is a unit and the length of the long part is a unit X, is arranged as a quadratic equation in the form x2 – x – 1 = 0, the solution of X gives the value (1 + √5)/2, which is the Golden Ratio.

The Golden Ratio arises in many different mathematical contexts. It can be drawn geometrically using a ruler and jib. It is also seen in the study of Archimedes and Platonic solids. Limit of consecutive numbers in a Fibonacci number sequence 1, 1, 2, 3, 5, 8, 13,… gives the Golden Ratio. The most basic continuous fraction is 1 + 1 / (1 + 1 / (1 + 1 / (1 + ⋯ the sum of its value is again the Golden Ratio.

The Golden Ratio is seen in modern mathematics fractals. Fractal are figures that share a common similarity in themselves and play an important role in the study of chaos and dynamical systems. One of the nice ways to show The Fi number is as follows: 50,5*0,5 + 0,5