Sometimes math is simply beautiful!

Let's talk about three of the most important numbers in math. They are so important that they got their own symbol.

First, there is \(\pi = 3.1415…\). \(\pi\) is the area of a circle with radius 1. It is also half the circumference of that circle. \(\pi\) is probably the first irrational number students learn about in school besides square roots: its decimal digits never end and do not repeat.

Another irrational number that is important enough to get its own symbol is the natural base \(e = 2.7182...\). \(e\) is used as the base of exponential functions that describe continuously compounded interest. An exponential function with base \(e\) is the most fundamental exponential function, because it is identical to its derivative.

And finally there is \(i\) which is the symbol for \(\sqrt{-1}\) and therefore essential for the set of complex numbers.

So here you have three numbers that play roles in completely different areas of math, two of which never end and one of them is not even real. You might think that these numbers have nothing to do with each other. But here comes the magic: The relationship between these numbers is

\(e^{i\pi}=-1\)

Isn't math beautiful!