Pi: Difference between revisions

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== The traditional concept ==
== The traditional concept ==
Standard mathematics says that π is the ratio between the circumference and the diameter of a [[Circle#The traditional concept|''perfect'' circle]]. It follows from this (after a nontrivial proof) that its notion of π is an irrational number---a number which cannot be written as a ratio of two whole numbers.
Standard mathematics says that π is the ratio between the circumference and the diameter of a [[Circle#The traditional concept|''perfect'' circle]].  
 
Standard mathematics "measures" this ratio using the methods of calculus.
 
Standard mathematics' notion of π is an irrational number---a number which cannot be written as a ratio of two whole numbers.

Revision as of 03:31, 21 January 2024

Pi, or π, is the ratio between the circumference and the diameter of a circle. The numerical value of π depends on context: which circle is under consideration, and how precise are one's measurements?

The traditional concept

Standard mathematics says that π is the ratio between the circumference and the diameter of a perfect circle.

Standard mathematics "measures" this ratio using the methods of calculus.

Standard mathematics' notion of π is an irrational number---a number which cannot be written as a ratio of two whole numbers.