Definition:Pi/Definition 2
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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:
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:
- $\pi \approx 11 \cdotp 00100 \, 10000 \, 11111 \, 1011 \ldots$