Pi
Open Issue on decimal expansion of Pi ...
Granted, it has been proven that the literal decimal expansion of Pi never cycles. However, I am wondering if there is a "deeper pattern" in the expansion which does, in fact, cycle. In other words, consider the sequence:
[012 123 234 345 456 567 678 789 8910 91011 101112 111213...]
Spaces are included above to make the pattern obvious. Without the spaces you would have:
[012123234345456567678789891091011101112111213...]
The digit-sequence above will not cycle. However, there is an obvious "pattern" in the sequence that repeats over and over, and I am wondering if there might be such a repeating pattern in Pi's decimal expansion (perhaps not such a short and simple one, but a pattern nevertheless). Or perhaps, the sequence of Pi is more or less just...random!
Anyway, has the issue I am discussing above been investigated for this wonderful irrational number ?? Thankyou...Mike Keith (lynne_mike@alltel.net)
:I'm open to correction, but as a mathematician I'd say it's highly unlikely. There's absolutely no reason to think it might be and it doesn't look right - not aesthetically consonant with the greater body of mathematics.
:There is no such pattern in the decimal expansion of pi. I have discovered a truly remarkable proof, but this talk page is too small to contain it. ^_~ Nextel ringtones Schneelocke/Schnee 15:38, 13 Jun 2004
:While there is no proof, Pi is usually considered to be normal, which would means there are no patterns
::Which would also imply that every finite pattern appears infinitely many times in the expansion? Majo Mills User:Sverdrup/
it looks like it's possible to simplify the fraction in the infinite sum by removing a k! factor. I think perhaps (4k)! was intended for (4k!). Can anyone confirm or disconfirm this guess? Free ringtones Eric119/Eric119 01:09, May 28, 2004
Yep, it is (4k)! (looked in the library). Its also already been changed Sabrina Martins Mrjeff/Mrjeff 12:54, 30 Jul 2004
Pi article title
When did the title start displaying as π ? - Mosquito ringtone Bevo/Bevo 23:26, 5 Jun 2004
That's even worse. Now I see a completely odd, non-Latin, non-Greek character. Abbey Diaz RickK/Rick'''Nextel ringtones User talk:RickK/K''' 02:01, Jun 6, 2004
Shanks
Shanks' famous calculation of π is listed twice in the history corresponding to two different years, 1853 and 1874. What's going on there? Majo Mills 4pq1injbok/4pq1injbok 19:01, 2 Jul 2004
BCE vs BC
Don't switch existing BCE usage to BC (or vice versa) without very good reason. This is the same as the issue of American vs. British spelling for words, and the precedent (leave usage as it is originally written) is the same. There are good arguments on either side (BCE is the academic/scholarly standard, even in British textbooks... and BC is more widely known, particularly outside North America) but until there is a Wikipedia standard on this issue (and there currently isn't) leave BCE/BC usage alone. Free ringtones Wclark/Wclark 18:38, 2004 Aug 29
:Well here are some very ''very'' good reasons for switching '''all''' BCE/CE to BC/AD, but first let me deal with your opinions. This is not the same issue as AE vs. BE. There is no controversy in usage of language versions, just personal preference usually based on country of origin, so the precedent 'leave as originally written' doesn't apply here. In fact, because there's no Wiki standard, not very much does apply, apart from NPOV. ''BCE is the academic/scholarly standard..''. Is it? I don't think so. It's certainly making inroads, particularly in internet writing originating from America, but it's virtually unknown in the rest of the world and is certainly not a standard in British text books.
:So why change?
:1)Quite simply because use of BCE/CE is 'POV'. The de-facto global standard is BC/AD. A minority in the USA are trying to push their politically correct alternative (and having some success) and to use it in Wikipedia is to support this minority standpoint. Maybe BCE/CE will eventually become the de-facto global standard. If it does, then Wikipedia should adopt it, but in the mean time it use here is, in effect, supporting a political objective. Wikipedia should not promote this usage.
:2)Wikipedia should not use terminlogy that most of the world does not understand. An article on pi is relevant to everyone the world over. Readers should not have to ask the question '.. what's all this BCE stuff?'. Sabrina Martins Arcturus/Arcturus 22:08, 29 Aug 2004
::BCE is not American ''Political Correctness'' it goes back several hundred years (the 15th century, I believe) and originated with Rabbinic scholars. BCE/CE '''and''' BC/AD are '''both''' POV, there's no escaping it. Nonetheless, BCE/CE is the academic standard in the English-speaking world (try to find a history textbook even a British one published in the last decade that still uses BC/AD). ''However'' in Wikipedia articles we still accept Standard units of measurement (''feet'', ''miles'', ''gallons'') despite the fact that the academic standard (even in the US) is to use Metric. So like I wrote earlier, there are good arguments on either side. Until there's a consensus (and the Cingular Ringtones Pi/Pi article isn't the place to form it), it's best to leave the BCE/BC usage as the original author wrote it. (And for the record, I personally use ISO date formats.) qelt the Wclark/Wclark 04:28, 2004 Aug 31
Historical values
The first two historical values for pi given are both in bold, and so were (presumably) both world records. However, the first one is actually closer to pi than the second. What's going on there?
:They were both in haitians on 20th century BC, so maybe it's because we don't know which one came first? huge increases Ugen64/ugen64 02:29, Sep 12, 2004
transcendental in 1885
the book i'm looking at (Chaos Theory, Peitgen Juergens Saupe) says that Lindemann proved pi transcendental in 1885, not 1882.
Def of constructible
The definition of a constructible real number is a number which lies in a field gotten by taken a finite sequence of quadratic extensions of the rationals, i.e. it's an x such that there are m1, m2, ..., mi, such that x is in Q[sqrt(m1), sqrt(m2), ..., sqrt(mi)]. (Sometimes the definition is taken to be geometric, but it's not much to show that this definition is equivalent.) Every constructible number is then "expressible as a finite number of integers, fractions, and square roots", (in fact, this is a defining property), so every constructible number is "expressible as a finite number of integers, fractions, and nth roots", and all of these numbers are algebraic. However, not all algebraic numbers can be expressed this way, (Galois theory). So, constructible > "exp. in finite # of int., frac., nth roots" > algebraic, but none of these implications is reversible. larger audience Revolver/Revolver 08:48, 7 Oct 2004
:OK, you're right. thanks -kingdom that User:Lethe/Lethe / weekend suggests User talk:Lethe/Talk
Pi and physics
''The reason it [π] occurs so often in physics is simply because it's convenient in many physical models.''
:Isn't one of the major reasons π occurs so often in physics simply because ''π occurs so often in Euclidean geometry and most of classical physics is based on models using Euclidean geometry''? dust by Revolver/Revolver 02:50, 2 Nov 2004
Pronunciation
While the original last grab Greek letter for pi was chosen commodity phonics/phonetically
equivalent to the English letter ''p'', it has now evolved to be
pronounced like the word ''pie'' in most circles.
Surely this should be up near the beginning of the article, not in the properties section. Furthermore, it is very poorly phrased: what it means to say is something like "Although in Greek the name of the letter π is/was pronounced something like the name of the english letter ''p'', the standard English pronunciation is identical to ''pie''." Furthermore, I'm not entirely sure that the Greek pronunciation is all that relevant to this article. I would make these changes myself, but frankly I'm having trouble coming up with a phrasing that isn't totally clunky and awkward. Someone else want to take care of this please? between gays 68.78.77.224/68.78.77.224 04:29, 22 Nov 2004 structured differently La:Usor:Iustinus/Iustinus
:Be bold. Fix it.
Greek word for π?
I read somewhere that in modern Greek, what we call π is called something else, but I can't for the life of me remember what it was. Does anyone else know, perchance? natured jabs GusGus/Gus 04:31, 2005 Jan 3
Break-up of digits?
Someone today just switched the digits of pi to a breakup of 3 digits each rather than the former 5 ie.
:3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58
:3.141 599 265 358 979 323 846 264 338 327 950 288 419 716 939 937 510 58
I think this second format is harder to read (personally I can't stand it), any input? Additionally the code is messed up with s radius of Nitrogenx/NitrogenX (Michael Hines) 05:22, Feb 25, 2005
Granted, it has been proven that the literal decimal expansion of Pi never cycles. However, I am wondering if there is a "deeper pattern" in the expansion which does, in fact, cycle. In other words, consider the sequence:
[012 123 234 345 456 567 678 789 8910 91011 101112 111213...]
Spaces are included above to make the pattern obvious. Without the spaces you would have:
[012123234345456567678789891091011101112111213...]
The digit-sequence above will not cycle. However, there is an obvious "pattern" in the sequence that repeats over and over, and I am wondering if there might be such a repeating pattern in Pi's decimal expansion (perhaps not such a short and simple one, but a pattern nevertheless). Or perhaps, the sequence of Pi is more or less just...random!
Anyway, has the issue I am discussing above been investigated for this wonderful irrational number ?? Thankyou...Mike Keith (lynne_mike@alltel.net)
:I'm open to correction, but as a mathematician I'd say it's highly unlikely. There's absolutely no reason to think it might be and it doesn't look right - not aesthetically consonant with the greater body of mathematics.
:There is no such pattern in the decimal expansion of pi. I have discovered a truly remarkable proof, but this talk page is too small to contain it. ^_~ Nextel ringtones Schneelocke/Schnee 15:38, 13 Jun 2004
:While there is no proof, Pi is usually considered to be normal, which would means there are no patterns
::Which would also imply that every finite pattern appears infinitely many times in the expansion? Majo Mills User:Sverdrup/
it looks like it's possible to simplify the fraction in the infinite sum by removing a k! factor. I think perhaps (4k)! was intended for (4k!). Can anyone confirm or disconfirm this guess? Free ringtones Eric119/Eric119 01:09, May 28, 2004
Yep, it is (4k)! (looked in the library). Its also already been changed Sabrina Martins Mrjeff/Mrjeff 12:54, 30 Jul 2004
Pi article title
When did the title start displaying as π ? - Mosquito ringtone Bevo/Bevo 23:26, 5 Jun 2004
That's even worse. Now I see a completely odd, non-Latin, non-Greek character. Abbey Diaz RickK/Rick'''Nextel ringtones User talk:RickK/K''' 02:01, Jun 6, 2004
Shanks
Shanks' famous calculation of π is listed twice in the history corresponding to two different years, 1853 and 1874. What's going on there? Majo Mills 4pq1injbok/4pq1injbok 19:01, 2 Jul 2004
BCE vs BC
Don't switch existing BCE usage to BC (or vice versa) without very good reason. This is the same as the issue of American vs. British spelling for words, and the precedent (leave usage as it is originally written) is the same. There are good arguments on either side (BCE is the academic/scholarly standard, even in British textbooks... and BC is more widely known, particularly outside North America) but until there is a Wikipedia standard on this issue (and there currently isn't) leave BCE/BC usage alone. Free ringtones Wclark/Wclark 18:38, 2004 Aug 29
:Well here are some very ''very'' good reasons for switching '''all''' BCE/CE to BC/AD, but first let me deal with your opinions. This is not the same issue as AE vs. BE. There is no controversy in usage of language versions, just personal preference usually based on country of origin, so the precedent 'leave as originally written' doesn't apply here. In fact, because there's no Wiki standard, not very much does apply, apart from NPOV. ''BCE is the academic/scholarly standard..''. Is it? I don't think so. It's certainly making inroads, particularly in internet writing originating from America, but it's virtually unknown in the rest of the world and is certainly not a standard in British text books.
:So why change?
:1)Quite simply because use of BCE/CE is 'POV'. The de-facto global standard is BC/AD. A minority in the USA are trying to push their politically correct alternative (and having some success) and to use it in Wikipedia is to support this minority standpoint. Maybe BCE/CE will eventually become the de-facto global standard. If it does, then Wikipedia should adopt it, but in the mean time it use here is, in effect, supporting a political objective. Wikipedia should not promote this usage.
:2)Wikipedia should not use terminlogy that most of the world does not understand. An article on pi is relevant to everyone the world over. Readers should not have to ask the question '.. what's all this BCE stuff?'. Sabrina Martins Arcturus/Arcturus 22:08, 29 Aug 2004
::BCE is not American ''Political Correctness'' it goes back several hundred years (the 15th century, I believe) and originated with Rabbinic scholars. BCE/CE '''and''' BC/AD are '''both''' POV, there's no escaping it. Nonetheless, BCE/CE is the academic standard in the English-speaking world (try to find a history textbook even a British one published in the last decade that still uses BC/AD). ''However'' in Wikipedia articles we still accept Standard units of measurement (''feet'', ''miles'', ''gallons'') despite the fact that the academic standard (even in the US) is to use Metric. So like I wrote earlier, there are good arguments on either side. Until there's a consensus (and the Cingular Ringtones Pi/Pi article isn't the place to form it), it's best to leave the BCE/BC usage as the original author wrote it. (And for the record, I personally use ISO date formats.) qelt the Wclark/Wclark 04:28, 2004 Aug 31
Historical values
The first two historical values for pi given are both in bold, and so were (presumably) both world records. However, the first one is actually closer to pi than the second. What's going on there?
:They were both in haitians on 20th century BC, so maybe it's because we don't know which one came first? huge increases Ugen64/ugen64 02:29, Sep 12, 2004
transcendental in 1885
the book i'm looking at (Chaos Theory, Peitgen Juergens Saupe) says that Lindemann proved pi transcendental in 1885, not 1882.
Def of constructible
The definition of a constructible real number is a number which lies in a field gotten by taken a finite sequence of quadratic extensions of the rationals, i.e. it's an x such that there are m1, m2, ..., mi, such that x is in Q[sqrt(m1), sqrt(m2), ..., sqrt(mi)]. (Sometimes the definition is taken to be geometric, but it's not much to show that this definition is equivalent.) Every constructible number is then "expressible as a finite number of integers, fractions, and square roots", (in fact, this is a defining property), so every constructible number is "expressible as a finite number of integers, fractions, and nth roots", and all of these numbers are algebraic. However, not all algebraic numbers can be expressed this way, (Galois theory). So, constructible > "exp. in finite # of int., frac., nth roots" > algebraic, but none of these implications is reversible. larger audience Revolver/Revolver 08:48, 7 Oct 2004
:OK, you're right. thanks -kingdom that User:Lethe/Lethe / weekend suggests User talk:Lethe/Talk
Pi and physics
''The reason it [π] occurs so often in physics is simply because it's convenient in many physical models.''
:Isn't one of the major reasons π occurs so often in physics simply because ''π occurs so often in Euclidean geometry and most of classical physics is based on models using Euclidean geometry''? dust by Revolver/Revolver 02:50, 2 Nov 2004
Pronunciation
While the original last grab Greek letter for pi was chosen commodity phonics/phonetically
equivalent to the English letter ''p'', it has now evolved to be
pronounced like the word ''pie'' in most circles.
Surely this should be up near the beginning of the article, not in the properties section. Furthermore, it is very poorly phrased: what it means to say is something like "Although in Greek the name of the letter π is/was pronounced something like the name of the english letter ''p'', the standard English pronunciation is identical to ''pie''." Furthermore, I'm not entirely sure that the Greek pronunciation is all that relevant to this article. I would make these changes myself, but frankly I'm having trouble coming up with a phrasing that isn't totally clunky and awkward. Someone else want to take care of this please? between gays 68.78.77.224/68.78.77.224 04:29, 22 Nov 2004 structured differently La:Usor:Iustinus/Iustinus
:Be bold. Fix it.
Greek word for π?
I read somewhere that in modern Greek, what we call π is called something else, but I can't for the life of me remember what it was. Does anyone else know, perchance? natured jabs GusGus/Gus 04:31, 2005 Jan 3
Break-up of digits?
Someone today just switched the digits of pi to a breakup of 3 digits each rather than the former 5 ie.
:3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58
:3.141 599 265 358 979 323 846 264 338 327 950 288 419 716 939 937 510 58
I think this second format is harder to read (personally I can't stand it), any input? Additionally the code is messed up with s radius of Nitrogenx/NitrogenX (Michael Hines) 05:22, Feb 25, 2005
posted at 6:42 PM
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