Pi - Revision history

Lfox at 01:44, 2 July 2024

2024-07-02T01:44:46Z

← Older revision		Revision as of 01:44, 2 July 2024
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	'''Pi''', or '''π''', is the [[ratio]] between the circumference and the diameter of a [[circle]]. π is not a number, because the numerical value of π depends on context: which circle is under consideration, and how precise are one's measurements? π should be thought of as more like a number-valued variable, which stands only for a specific, limited, class of things.		'''Pi''', or '''π''', is the [[ratio]] between the circumference and the diameter of a [[circle]]. π is not a number, because the numerical value of π depends on context: which circle is under consideration, and how precise are one's measurements? π should be thought of as more like a number-valued variable, which stands only for a very specific, limited, class of things.

	== The traditional concept ==		== The traditional concept ==

2024-07-02T01:44:18Z

← Older revision		Revision as of 01:44, 2 July 2024
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	'''Pi''', or '''π''', is the [[ratio]] between the circumference and the diameter of a [[circle]]. π is not a number, because the numerical value of π depends on context: which circle is under consideration, and how precise are one's measurements? π should be thought of as more like a variable, which stands only for a specific, limited, class of things.		'''Pi''', or '''π''', is the [[ratio]] between the circumference and the diameter of a [[circle]]. π is not a number, because the numerical value of π depends on context: which circle is under consideration, and how precise are one's measurements? π should be thought of as more like a number-valued variable, which stands only for a specific, limited, class of things.

	== The traditional concept ==		== The traditional concept ==

2024-07-02T01:44:00Z

← Older revision		Revision as of 01:44, 2 July 2024
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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]]. π is not a number, because the numerical value of π depends on context: which circle is under consideration, and how precise are one's measurements? π should be thought of as more like a variable, which stands only for a specific, limited, class of things.

	~~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 ==

2024-04-25T19:55:26Z

← Older revision		Revision as of 19:55, 25 April 2024
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	where the "..." signifies that the digits go on forever.		where the "..." signifies that the digits go on forever.

			== Examples ==
			π shows up in many places, besides just circles.

			a disk of radius <math>r</math> has area <math>\pi r^2</math>

			a cone with height <math>h</math> and with base of radius <math>r</math>, has area <math>\frac{1}{3}\pi r^2 h</math>

			a sphere of radius <math>r</math> has volume <math>\frac{4}{3} \pi r^3</math>, and surface area <math>4 \pi r^2</math>

			the area under a Gaussian distribution is proportional to some power of <math>\pi^{1/2}</math>.

2024-04-22T22:26:18Z

← Older revision		Revision as of 22:26, 22 April 2024
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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 ==

2024-02-03T23:31:24Z

delete me

← Older revision		Revision as of 23:31, 3 February 2024
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	where the "..." signifies that the digits go on forever.		where the "..." signifies that the digits go on forever.

	~~== delete me ==~~
	~~editing stuff to try to get it to crash <math>\mathbb{Q} \rightarrow \int_0^\infty \frac{\Gamma(x + i\epsilon + y)\Gamma(z + x)}{\Gamma(x - z)} dx</math>~~

	~~blahblahblah <math>a</math> <math>b</math> <math>c </math> <math>\int \int \int \int \int 1\int \int \sqrt{ } sdaf </math>~~

	~~sadlkfjklsdajflkajsdflkasj asldfjlsk l asdlkjd sflj sfkljsfl jlkasfjlkasfj~~

	~~fasdljafs lk alfsk jjs dflkja~~

	~~lkasdjf l j aslfdjlkfd jlkasfdj lksafj. sd~~

	~~asd lsaj lkjf ljf asdflkj lkasdjf dfsal safj lkjas jlksdjfsadlkfjla ksf;fa j;lsdjfals;kfj asdlkf jasdl;f~~

	~~lasdfj las'dkjf las;kfj asdl;kfj a~~

2024-01-27T23:44:45Z

delete me

← Older revision		Revision as of 23:44, 27 January 2024
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	blahblahblah <math>a</math> <math>b</math> <math>c </math> <math>\int \int \int \int \int 1\int \int \sqrt{ } sdaf </math>		blahblahblah <math>a</math> <math>b</math> <math>c </math> <math>\int \int \int \int \int 1\int \int \sqrt{ } sdaf </math>

			sadlkfjklsdajflkajsdflkasj asldfjlsk l asdlkjd sflj sfkljsfl jlkasfjlkasfj

			fasdljafs lk alfsk jjs dflkja

			lkasdjf l j aslfdjlkfd jlkasfdj lksafj. sd

			asd lsaj lkjf ljf asdflkj lkasdjf dfsal safj lkjas jlksdjfsadlkfjla ksf;fa j;lsdjfals;kfj asdlkf jasdl;f

			lasdfj las'dkjf las;kfj asdl;kfj a

2024-01-27T23:43:39Z

delete me

← Older revision		Revision as of 23:43, 27 January 2024
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	== delete me ==		== delete me ==
	editing stuff to try to get it to crash <math>\mathbb{Q} \rightarrow \int_0^\infty \frac{\Gamma(x + i\epsilon + y)\Gamma(z + x)}{\Gamma(x - z)} dx</math>		editing stuff to try to get it to crash <math>\mathbb{Q} \rightarrow \int_0^\infty \frac{\Gamma(x + i\epsilon + y)\Gamma(z + x)}{\Gamma(x - z)} dx</math>

			blahblahblah <math>a</math> <math>b</math> <math>c </math> <math>\int \int \int \int \int 1\int \int \sqrt{ } sdaf </math>

2024-01-27T23:37:09Z

← Older revision		Revision as of 23:37, 27 January 2024
Line 13:		Line 13:

	where the "..." signifies that the digits go on forever.		where the "..." signifies that the digits go on forever.

			== delete me ==
			editing stuff to try to get it to crash <math>\mathbb{Q} \rightarrow \int_0^\infty \frac{\Gamma(x + i\epsilon + y)\Gamma(z + x)}{\Gamma(x - z)} dx</math>

2024-01-21T03:34:16Z

The traditional concept

← Older revision		Revision as of 03:34, 21 January 2024
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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]].		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 "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.		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.