Pi

Definition

Pi is an irrational number denoted by the greek letter $\displaystyle \pi$ . It is the ratio of a circle's circumference, or perimeter, to its diameter. It is roughly equal to 3.141592653. The number pi is one of the most important constants in all of mathematics and appears in some of the most surprising places, such as in the sum $\sum_{n=1}^\infty \frac{1}{n^2}=\frac{\pi^2}{6}$ . The fractional approximation for pi (not exact) can be $\frac{22}{7}$ . An exact formula for pi is $4\left( \sum_{i = 0}^\infty (-1)^i \left(\frac{1}{2n+1}\right)\right)$ .

The number pi often shows up in problems in number theory, particularly algebraic number theory. For example, many class number formulae involve pi.

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Pi

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