Miracle of Euler
Euler's miracle is the calculation of the principal value for
i i = e− π / 2 or approximately 0.207879576…
Explanation
By substitution of in Euler's formula
you get
If you calculate this you come up with
It is a transcendent number. So there are infinitely many decimal places, which never form a regular pattern. You can therefore add the number to the sequence with π and e. The imaginary unit has no real value, but still
and therefore just lies on the number line.
HistorySwiss mathematician Leonhard Euler described this calculation in 1748. |