Question

How does e relate to `pi`?

Answer 1

These two numbers are not related. At least, they were not related at inception (`pi` is much-much older, goes back to the beginning of geometry, while `e` is a relatively young number related to a theory of limits and functional analysis).

This does not exclude certain not very obvious cases where their relationship does exist. I don't have examples off the top of my head, but allow the possibility of their existence.

There is also a statement (which is not true) that `e^pi = pi^e`. Admittedly, these two expressions are really close in value, but they are not equal.

Answer 2

The famous equation involving both `e` and `pi` is Euler's identity:

`e^(i pi) +1 = 0`

where `i` is the imaginary unit. (So `i^2 = -1`.)

Also rendered as

`e^(i pi) = -1`