\begin{definition}[Definition:Pi/Definition 2]
The real number $\pi$ (pronounced '''pie''') is an irrational number (see proof here) whose value is approximately $3.14159\ 26535\ 89793\ 23846\ 2643 \ldots$
The real functions sine and cosine can be shown to be periodic.
The number $\pi$ is defined as the real number such that:
:the period of both sine and cosine is $2 \pi$.
\end{definition}