[So Cal Rocket]

As a corollary to Euler’s theorem, it fascinates me that:

e^(pi x i) = -1

The fact that three somewhat unrelated concepts such as e, pi and i can be put together to make such an elegant formula blows me away.

[FredZarguna]

Here is a little rhyme I used to recite to my students:

It is a remarkable fact
that i to the i
is the same thing
as the square root of one
divided by e to the pi.

That is: iⁱ = √(1/e^π)

This is a remarkable equation, in that 1) a pure imaginary raised to itself is a pure real number 2) the result contains arguably all of the most fundamental constants in mathematics: i, e, π, 1, (and implicitly, 2).