25 February 2017

Square root of three

\(\sqrt {3}\) is also known as Theodorus' constant, due to the Greek mathematician Theodorus of Cyrene who proved that the square roots of numbers from \(3\) to \(17\), excluding the \(4\), the \(9\) and the \(16\), were irrational numbers.

It is also the spatial diagonal of a cube whose edges measures a unit.

And yet:

\(\sqrt {3}=2\sin\left( \frac{\pi}{3}\right)\)

\(\sqrt {3}=2\cos\left( \frac{\pi}{6}\right)\)

\(\sqrt {3}=\tan\left( \frac{\pi}{3}\right)\)

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