Changes: Pi

Revision as of 03:25, 26 April 2018

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Pi, the 16th Greek letter, lowercase π, uppercase Π, can refer to:

pi (constant) - π ≈ 3.141592653589793238462643383279502884197169399375105820974944592307816406286208..., an irrational number representing the ratio of a circle's circumference to its diameter (also known as Archimedes' number)
Product operator Π — e.g., $\prod _{i=0}^{n}f(i)$ . (See also product of a sequence.) It is functionally similar to summation notation, using $\sum _{i=0}^{n}$ , which is the sum of a sequence.
Prime counting function π(x). (See also prime numbers.) A function defined to return a value equal to the quantity of prime numbers less than or equal to its inputted value. (eg $\pi (8)=4$ since only four numbers: 2,3,5,7 are all the prime numbers less than or equal to 8.)
The transformation (horizontal shift) of the Gamma function: $\Pi(x)=\Gamma(x+1)$ $\Pi (x)=\Gamma (x+1)$ .
- The reciprocal of its capitalized counterpart: $\pi (x)={\frac {1}{\Pi (x)}}$ .
The upside down capital represent Coproducts: $\coprod _{j\in J}$

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+{{Disambig}}
-'''Pi''', the 16<sup>th</sup> [[Greek letter]], written in lowercase as &pi; and capitalized as &Pi; (sometimes written <math>\mathrm{][}</math>), can refer to the following mathematical concepts.
+'''Pi''', the 16th [[Greek letter]], lowercase π, uppercase Π, can refer to:
-* [[pi (constant)]] - <math>\pi \approx 3.14159\ldots</math>, representing the ratio of a circle's circumference to its diameter (also known as Archimedes' number)
-* [[Product operator]] &Pi; — e.g., <math>\prod_{i=0}^n f(i)</math>. (See also [[product of a sequence]].) It is functionally similar to [[summation notation]], using <math>\sum_{i=0}^n</math>, which is the sum of a sequence.
+* [[pi (constant)]] - <span style="font-family: serif">π</span> ≈ 3.141592653589793238462643383279502884197169399375105820974944592307816406286208..., an [[irrational number]] representing the ratio of a circle's circumference to its diameter (also known as Archimedes' number)
-* [[Prime counting function]] &pi;(x). (See also [[prime number]]s.) A function defined to return a value equal to the quantity of prime numbers less than or equal to its inputted value. (eg <math>\pi(8) = 4</math> since only four numbers: 2,3,5,7 are all the prime numbers less than or equal to 8.)
+* [[Product operator]] <span style="font-family: serif">Π</span> — e.g., <math>\prod_{i=0}^n f(i)</math>. (See also [[product of a sequence]].) It is functionally similar to [[summation notation]], using <math>\sum_{i=0}^n</math>, which is the sum of a sequence.
+* [[Prime counting function]] π(x). (See also [[prime number]]s.) A function defined to return a value equal to the quantity of prime numbers less than or equal to its inputted value. (eg <math>\pi(8) = 4</math> since only four numbers: 2,3,5,7 are all the prime numbers less than or equal to 8.)
 * The transformation (horizontal shift) of the [[Gamma function]]: <math>\Pi(x) = \Gamma(x+1)</math>.
 ** The reciprocal of its capitalized counterpart: <math>\pi(x) =\frac{1}{\Pi(x)}</math>.
 * The upside down capital represent [[Coproduct]]s: <math>\coprod_{j \in J}</math>
 [[Category:Symbols]]
+[[Category:Numbers]]
+[[Category:Irrational numbers]]
+[[Category:Transcendental numbers]]