Though Euler’s Identity follows from the polar form of complex numbers, it is impossible to derive the polar form (in particular the spontaneous appearance of the number e) without calculus.

Both are “transcendental” quanti­ties; in decimal form, their digits ... But the weirdest thing about Euler’s formula—given that it relies on imaginary numbers—is that it’s so ...

To a nonmathematician, having the letter “i” represent a number that does not quite exist and is “imaginary” can be ... one equation to rule them all: Euler’s 1740 formula.