## 12 May 2018

### Square root of two

$\sqrt 2$ is the length of the diagonal of a square whose side measures a unit, also known as Pythagoras' constant, it is an irrational number.

Historically, the first object that registers an approximation of the $\sqrt 2$ was the Babylonian clay tablet, which now belongs to the Yale Babylonian Collection, Yale University (USA). The object has been dated between $1,800$ BC and $1,600$ BC and it has a good approximation of $\sqrt 2$: $1+\frac{24}{60}+\frac{51}{60^2}+\frac{10}{60^3}$.

Some interesting properties of $\sqrt 2$:

$\sqrt 2=2 \times \sin 45º$

$\sqrt 2=2 \times \cos 45º$

$\sqrt 2=\frac{\sqrt i+i \sqrt i}{i}$

$\sqrt 2=\frac{\sqrt {-i}-i \sqrt {-i}}{-i}$

$\sqrt 2=1+\frac{1}{2+\frac{1}{2+\frac{1}{2+\frac{1}{2+\ddots}}}}$