Difference between revisions of "Pi"
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== Definition == | == Definition == | ||
| − | '''Pi''' is an [[irrational]] number denoted by the greek letter <math>\displaystyle \pi </math>. 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 | + | '''Pi''' is an [[irrational]] number denoted by the greek letter <math>\displaystyle \pi </math>. 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 [[constant]]s in all of mathematics and appears in some of the most surprising places, such as in the sum <math>\sum_{n=1}^\infty \frac{1}{n^2}=\frac{\pi^2}{6}</math>. The fractional approximation for pi (not exact) can be <math>\frac{22}{7}</math>. An exact formula for pi is <math>4\left( \sum_{i = 0}^\infty (-1)^i \left(\frac{1}{2n+1}\right)\right) </math>. |
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| + | The number pi often shows up in problems in [[number theory]], particularly [[algebraic number theory]]. For example, many [[class number]] formulae involve pi. | ||
== See Also == | == See Also == | ||
*[[Circle]] | *[[Circle]] | ||
Revision as of 23:09, 24 June 2006
Definition
Pi is an irrational number denoted by the greek letter 
. 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 
. The fractional approximation for pi (not exact) can be 
. An exact formula for pi is 
.
The number pi often shows up in problems in number theory, particularly algebraic number theory. For example, many class number formulae involve pi.
