- Drafting
- BBC News World

**During the centuries that China, India, and the Islamic empire had been on the rise, Europe had fallen under a shadow. **

All intellectual life, including the study of mathematics, had come to a standstill.

But in the 13th century, things were beginning to change.

Led by Italy, Europe began to explore and trade with the Orient.

With that contact came the diffusion of eastern knowledge to the west.

And it would be the son of a customs officer who would become **Europe’s first great medieval mathematician**.

## A badly received import

As a child, he traveled through North Africa with his father, where he learned about the developments of Arabic mathematics and especially the benefits of Indo-Arabic numbers.

When he arrived in Italy, he wrote a book that would be of great influence on the development of Western mathematics.

That mathematician was Leonardo de Pisa, better known as Fibonacci, and in his “Calculation Book”, Fibonacci **promoted the new number system**, showing how simple it was compared to the Roman numerals that were used throughout Europe.

The calculations were much easier, something tremendously important to anyone who dealt with numbers, from mathematicians to merchants.

However, what the numbers brought from the East aroused was distrust, not joy or relief.

Old habits are hard to break.

Some believed that they would be more exposed to fraud, that they lent themselves to being manipulated.

Others thought they were so easy to use for calculations that they would empower the masses, taking authority away from intellectuals who knew how to use the old-fashioned numbers.

The city of** Florence even banned them in 1299**.

But over time, common sense prevailed, the new system spread throughout Europe, and the old Roman system slowly died out.

## The enigma of rabbits

Finally, the Hindu-Arab numbers, from 0 to 9, triumphed.

Today, Fibonacci is best known for discovering a few numbers, now called **the fibonacci sequence**, which arose when I was trying to solve a riddle about the mating habits of rabbits.

Suppose a farmer has a pair of rabbits.

It takes two months for rabbits to reach maturity, and after that they give birth to another pair of rabbits every month.

The problem was **excuse me ****know**** how many pairs of rabbits** there would be in a given month.

- During the 1st month you have a couple of rabbits and, since they have not matured, they cannot reproduce.
- During the 2nd month, there are still
**only one par**. - But at the beginning of the 3rd month, the first pair reproduces for the first time, so there is
**2****pairs of rabbits.** - At the beginning of the 4th month, the first pair reproduces again, but the second pair is not mature enough, so there is
**3****pairs**. - In the 5th month, the first pair reproduces and the second pair reproduces for the first time, but the third pair is still very young, so there are
**5****pairs**.

The mating ritual continues, but what you will soon notice is that the number of pairs of rabbits you have in a given month **is the sum of the pairs of rabbits you have had in each of the two previous months**, so the sequence continues …

1 … 1 … 2 … 3 … 5 … 8 … 13 … 21 … 34 … 55 … and so on.

## The favorites

It turned out that Fibonacci numbers are nature’s favorite numbers.

**Not just rabbits** they use them.

The number of petals in a flower is invariably a Fibonacci number. If you count the segments of the pineapples up and down you will find them. Even snails use them to grow their shells.

Wherever you find growth in nature, you will find Fibonacci numbers.

The Fibonacci sequence is also the mathematical prime of the golden number, **a number that has haunted human culture for thousands of years**.

## golden number

If you divide any number in the Fibonacci sequence by the previous one, for example, 55/34, or 21/13, and the answer is always close to **1.61803**.

And that is why the Fibonacci sequence is also known as the golden sequence, because that 1.61803 is what is known as **the golden number****.**

It is a special number found by dividing a line into two parts, so that the longest part (a) divided by the smallest part (b) equals the total length divided by the longest part.

Often the golden number is symbolized using * phi*, the 21st letter of the Greek alphabet.

In an equation form, it looks like this:

Those numbers can be applied to the proportions of a rectangle, called **the golden rectangle**, considered one of the most visually satisfying geometric shapes.

The golden rectangle is also related to **the golden spiral**, which is created by making adjacent squares of Fibonacci dimensions.

But for those of us who are beginners, perhaps it is easier to understand if we think about it in terms of design.

## Many names

The golden number has been discovered and rediscovered many times, and that is why it has so many names: **golden number, extreme and mean ratio, golden ratio, golden ratio, golden mean, golden ratio and divine ratio**.

Historically, it is expressed in the architecture of many ancient creations.

In the Great Pyramid of Giza, for example, the length of each side of the base is 230 meters with a height of 146 meters. The ratio of the base to the height is approximately 1.575, very close to the golden number.

Phidias (500 BC – 432 BC), the famous Greek sculptor and mathematician, is believed to have applied *phi* to the design of sculptures for the Parthenon.

## From “The Last Supper” to Twitter

“Without mathematics there is no art”, assured Luca Pacioli who, in 1509, published “*Of the divine proportion*“, illustrated by none other than Leonardo da Vinci.

“*Of the divine proportion*“It is a mathematics book, but from the first page Pacioli affirms that his intention is to reveal to artists the secret of harmonic forms through the use of divine proportion.

And in fact, there are those who think that the golden number is the essence of beauty in the proportions of the paintings of Da Vinci, who called it *sectio aurea*.

They claim that he used it to define all the proportions in his “Last Supper”, “Vitruvian Man” and “Mona Lisa”.

The use of this divine proportion has also been noted in works by Michelangelo, Raphael, Rembrandt, Seurat, Salvador Dalí … and even in the Twitter logo.

## We carry it inside

But you don’t even have to leave home to find that golden number: our bodies and faces follow that mathematical ratio.

**L****to the length of our fingers**, each section from the tip of the base to the wrist is larger than the previous one by approximately the proportion of*phi*.- The measure of the distance of the
**belly button**human to the ground and from the top of the head to the navel is the golden ratio. **U****in the DNA molecule**it measures 34 angstroms by 21 angstroms in each complete cycle of the double helix spiral. In the Fibonacci series, 34 and 21 are successive numbers.

And apparently our brains are programmed to prefer objects and images that use divine proportion.

Several studies have shown that when test volunteers are asked to look at a random series of faces, and pick the ones they find most attractive – despite my unfamiliar mathematicians and physicists being *phi**–* They choose those that show golden proportions between the width of the face and the width of the eyes, nose and eyebrows.

**It’s almost a subconscious attraction**.

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Eddie is an Australian news reporter with over 9 years in the industry and has published on Forbes and tech crunch.