Pi: Difference between revisions
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'''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? | '''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? | ||
I think [TODO] that π should be thought of not as a number, but as a class of numbers, each number arising from the real circumference/diameter of a real circle. | |||
== The traditional concept == | == The traditional concept == | ||
Revision as of 22:26, 22 April 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?
I think [TODO] that π should be thought of not as a number, but as a class of numbers, each number arising from the real circumference/diameter of a real circle.
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.
Thus in standard mathematics,
π = 3.141592653589793238462643383279502884197169399375105 8209749445923078164062862089986280348253421170679...
where the "..." signifies that the digits go on forever.