Miracle of Euler
The miracle of Euler is the principle value of i raised to the power of i
i i = e− π / 2 or approximately 0.207879576…
Explanation
From the definition of the logarithm follows that you can write any number as an exponential function, so that
where k ∈ ℤ, the set of integers.
The principle value (for k = 0) is e− π / 2 or approximately 0.207879576...
HistoryThe Swiss mathematician Leonhard Euler described this calculation in 1748. |