# Make this definition of pi work

## Main Question or Discussion Point

I quite like the following definition of pi and I wonder which minimal algebraic rules are needed to make this definition work?

$$\lim_{n\to\infty}\left(1+\frac{a}{n}\right)^n=1$$
$$\therefore |a|=2\pi k$$

(For example, are there algebras more general than complex numbers, where this works?)

Well, in the quaternions $e^{2\pi u} = 1$ where $u$ is any quaternion with $u^2 = -1$