The golden number might have been the first irrational number known to the Greeks. When the Pythagoreans discovered that irrational numbers existed, i.e. that they could not be written as the quotient of two whole numbers, they were dismayed, as this fact broke many of their philosophical theories. That is why they decided to keep this discovery a secret.

Theano of Crotone, a Pythagorean mathematician, was the first woman to carry out these divisions, confirming thus the existence of irrational numbers. As a good Pythagorean, she believed and defended that all material objects were composed of natural numbers, so that the measure of anything could be expressed with an exact measure. However, she was also the first to posit the existence of the golden ratio as the essence of the universe.

The golden number, or golden ratio, is represented with the Greek letter Φ (Phi), honouring Phidias. Remember that Phi is a proportion in which "The whole is to the part as the part is to the remainder". The following image shows an example:

1. Let's find now the golden number. We assume that the smaller segment is 1 cm, and that we do not know the value of the larger one, i.e. a = x and b = 1. Then, the whole segment measures x+1, and we can state the above relationship as:

If we multiply crosswise, we obtain the following quadratic equation:

Solve the equation to get x, which will be the golden number, also called the "divine proportion''.

2. Use your ruler to obtain the measurements of a credit card and an ID card (8.6 cm long, 5.4 cm wide) and check that they are in the same proportion as the golden ratio. 

3. In ancient times, beauty was related to this proportion and this is still used today as it is thought that it makes objects more attractive. Bearing in mind that all bodies are valid in their different shapes and sizes, check if your height is in this proportion to the distance from the ground to your belly button.