# How does e relate to pi?

Apr 27, 2015

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.

Apr 27, 2015

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

${e}^{i \pi} = - 1$