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 \(\sqrt 2\):

\(\sqrt 2=2 \times \sin 45º\)

\(\sqrt 2=2 \times \cos 45º\)

\(\sqrt 2=\frac{\sqrt i+i \sqrt i}{i}\)

\(\sqrt 2=\frac{\sqrt {-i}-i \sqrt {-i}}{-i}\)

\(\sqrt 2=1+\frac{1}{2+\frac{1}{2+\frac{1}{2+\frac{1}{2+\ddots}}}}\)

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