# Golden number

The **golden number** , or **F number** as it is also known, was the first **rare number** or in other words an **irrational** number that was discovered many years ago by Greek mathematicians. The golden number, which is also known as the ** “golden number”** or

*, is a constant that we can*

**“divine proportion”****observe**and

**perceive**on a daily basis, although most of the time we are not aware of it. We can see it in the

**proportions**of buildings, paintings, sculptures, and even in the human body.

## What is the golden number?

The golden number is an **irrational ****algebraic** number that has great properties of **relation** and **proportion** between two **segments** on a **line** , in other words, within a **geometric construction** and we also find it in **nature** .

- Definition
- Characteristics of the golden number
- Source
- History
- Who discovered it
- Properties
- Applications of the golden number
- How much does it cost
- How it is represented
- Importance
- Examples
- Curiosities

## Definition

The golden number is an **algebraic number** that have different **properties** and that was discovered in **ancient times** , as a ratio or proportion. This proportion can be found in some **geometric figures** and also in **nature** in elements such as shells, ribs of the leaves of some trees, the thickness of the branches, etc.

Throughout history , the golden number has been attributed great importance in various works of **architecture** and in other **arts** , although some of these cases have been objectionable to **mathematics** and **archeology** . In other words, it is the **point** at which the **arts** and **mathematics meet** .

## Characteristics of the golden number

Some of the main characteristics of the golden number are the following:

- The golden number is an
**irrational algebraic**number . - The decimal representation of the number
**has no period**. - The ratio of the golden number can be found in some
**geometric figures**and also in nature. - The number is represented by the Greek letter φ (phi).
- It is also known as an
**irrational**or**decimal**algebraic number with no period. - Its
**mathematical value**is approximately 1.618. - It is also known as the golden number, extreme and average ratio, golden ratio, golden ratio, golden mean, golden ratio, divine section, golden section, divine proportion.

## Source

Many scholars think that it originated in **Babylon** and **Assyria** from around **2000 BC. C.** although there is no historical documentation that shows us that it was used in the elaboration of the **stelae** . It is believed that the origin of the number was born from a formal **study** done by **Euclid** who thought that it was a **line** that had been **cut** in **extreme** and **average ratio** when the line was whole.

## History

The first to make a formal study of the golden number was **Euclid** who showed that the number could not be described as the **ratio** of two **whole numbers** ; in other words, it was an irrational number. In 1509 the Italian mathematician and theologian **Luca Pacioli** published **De Divina Proportione** raises **some reasons** why he considers it appropriate to consider the golden number divine:

- The
**uniqueness**; for he compared it to the oneness of God. - It is defined by three
**line segments**, and that is why it is associated with the Trinity. - The
**incommensurability**that was equivalent to the incommensurability of God. - The
**self-similarity**associated with the golden number compared to the omnipresence and invariability of God.

The first use of the adjective aureo, gold, or gold, to refer to a number is made by the German mathematician **Martin Ohm** , in the second edition of 1835 of his book **Die Reine Elementar Matematik** .

## Who discovered it

**Leonardo Fibonacci** , was the one who discovered the series that leads us to **phi** . In the 12th century, it was he who discovered a simple **number series that** would be the basis of the incredible relationship that we find behind phi. Starting with 0 and 1, each number in the series is simply the sum of the previous two.

## Properties

Some of the properties of the golden number are:

- One of its most important
**arithmetic properties**is that its**square**(Φ^{2}= 2.61803398874988…) and its inverse (1 / Φ = 0.61803398874988…) have the same infinite decimal places. - Another of its properties is that an
**aesthetic character**is attributed to objects whose measurements keep the golden ratio.

## Applications of the golden number

This number has been applied to various **works of art** , for example the **Parthenon** , we also find it in proportions of the **golden rectangle** and in the **UN** building You can see examples of golden rectangles we can find them on **credit cards** , in our **card** identity cards and also on tobacco packs

## How much does it cost

The golden number has a value close to **1,618.**

## How it is represented

The golden number is the numerical value of the proportion between two line segments a and b and that meet the following relationship:

**(a + b) / a = a / b**

## Importance

It is important because we even find it in some **geometric figures such** as shells, ribs of the leaves of some trees, the thickness of the branches, etc. It also has an aesthetic character of the objects that follow the **golden ratio** , as well as a **mystical** importance . In history, it has been given great importance in **architecture** and other arts, although some of these cases have been objectionable to **mathematics** and **archeology** .

## Examples

**Architecture**

- The pyramids of Cheops
- Eiffel Tower
- In the parthenon

**In nature**

- On the sheets
- On the planets of the solar system
- In the morphological proportions of bees

**In art**

- Gioconda, painted by Leonardo.

**In music**

- Mozart piano sonatas.
- Beethoven’s Fifth Symphony.

**In the human body**

- Between the height of the man and the distance from the navel to the tip of the hand is the golden number.
- The teeth grow according to the golden ratio.

## Curiosities

It has had many different names, but its symbol makes it **unequivocal** as it is the Greek letter phi, in honor of the Greek sculptor **Phidias** , whose works were considered the closest to aesthetic **perfection** , as is the golden ratio.

One of the reasons why the golden number has fascinated those who study it is that it is found **naturally** in the most unexpected places. For example, the ratio **bees female** and **male** in a **hive** is generally similar to the golden ratio.