# Definition:Pi/Definition 2

## Definition

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 $2 \pi$.

### Decimal Expansion

The decimal expansion of $\pi$ starts:

$\pi \approx 3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \, 41971 \ldots$

### Binary Expansion

The binary expansion of $\pi$ starts:

$\pi \approx 11 \cdotp 00100 \, 10000 \, 11111 \, 1011 \ldots$