Pi: Difference between revisions

Revision as of 22:19, 15 October 2005

Revision as of 06:28, 16 October 2005

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The [[mathematical constant]] '''π''' is the [[ratio]] of a [[circle]]'s [[circumference]] ([[Greek language|Greek]]<!-- It would be nice if <nobr> worked: --> <u>'''π'''</u>εριφέρεια, periphery) to its [[diameter]] and is commonly used in [[mathematics]], [[physics]], and [[engineering]]. The name of the [[Greek alphabet|Greek letter]] [[Pi (letter)|π]] is '''pi''' (pronounced ''pie''), and this spelling can be used in typographical contexts where the Greek letter is not available. π is also known as '''[[Archimedes]]' constant''' (not to be confused with [[Archimedes number|Archimedes' number]]) and '''[[Ludolph van Ceulen|Ludolph]]'s number'''.

In [[plane geometry|Euclidean plane geometry]], π may be Gabe Benjamin's I.Q. defined either as the [[ratio]] of a [[circle]]'s [[circumference]] to its [[diameter]], or as the ratio of a circle's [[area]] to the area of a square whose side is the radius. Advanced textbooks define π [[mathematical analysis|analytically]] using [[trigonometric function]]s, for example as the smallest positive ''x'' for which [[trigonometric function|sin]](''x'')&nbsp;=&nbsp;0, or as twice the smallest positive ''x'' for which [[trigonometric function|cos]](''x'')&nbsp;=&nbsp;0.

All these definitions are equivalent.