I think it would be nice to add one or two new rows for the computability / definability of each constant. What do you think? —Preceding unsigned comment added by 134.184.131.153 ( talk) 10:40, 6 September 2007 (UTC)
Should Chaitin's "constant" be here? It's not actually a real number until you've chosen a computational machine, and I'm not aware of any canonical choices for that. For any such choice, on the other hand, we can make some statements about Ω. For example, for any machine for which the string "0" is a program that simply terminates, Ω > 0.5. We might even know the first digit.
Prumpf 14:37, 14 Aug 2004 (UTC)
Is there any reason why and are listed as irrational rather than algebraic? Gkhan 16:45, Sep 7, 2004 (UTC)
Is the number 1 not a mathematical constant? It is used to define the set of natural numbers. -- Lambyuk 01:44, 13 May 2005 (UTC)
Err, 1 and 0 are not constants. They are numbers. In software development, for example, 0 is a literal, but A=0 would mean A is a constant representing number 0. Secondly, if we have 0 and 1, why not 2, 3 and 4? How about 0x0a? How about 20? It is also very interesting...
Similarly, i is the same as 1 but for the complex plane. Just a unit, nothing special. —Preceding unsigned comment added by 216.55.199.86 ( talk) 20:43, 14 February 2008 (UTC)
I've redone the table in (I hope) a better looking format. It is similar to format used on Table of mathematical symbols. Any comments? Paul August ☎
Some of the table rows need to be bigger. I would do it myself, but I don't want to mess it up. -Mihirgk
Right? (Are all constants that are irrational-but-not-transcendent algebraic?)
Is Mill's constant symbolised by theta (as in the table) or phi (as in it's seperate article)? -- Saboteur 01:11, 31 March 2006 (UTC)
Accoring to this article,D(1)=6/pi^2,not the HSM constant. It uses sigma for the HSM. We should change the symbol.
I just changed the symbol.
Is the Erdos-Borwein constant really algebraic? You should make something called I. It will mean "known to be irrational,may be algebraic or transcendental." That would be a good extra symbol.
Most precise does not equal most accurate. "Number of known digits" as used in this table means number of digits known to be correct, not number of digits that could be right. Fredrik Johansson 22:57, 6 September 2006 (UTC)
The article "
http://en.wikipedia.org/wiki/Cahen%27s_constant" give the following value :
0.64341054629...
What is the true value ?
cf [1]
Papy77
15:41, 1 February 2007 (UTC)
Is Mathematical constint a good redirect? Con stint 12:27, 27 February 2007 (UTC)
There are so many red links in the table. We should create some pages and remove the external links. Math Maniac 11:46, 1 March 2007 (UTC)
I would like to see if anyone can further expand upon my attempts of researching the following value. Sloan's A037077 ie. one of two real decimal expansions of 1^(1/1)-2^(1/2)+3^(1/3)... or a generalized sum to the divergent series. http://www.research.att.com/~njas/sequences/A037077 [2] This constant remains a mystery. For instance, before 1998 what was the computation-history of the value that is presently called the MRB Constant? What is the closed form expression (assuming it exists) for the value of this constant? What relation does this constant of infinite dimensional “ hypercubes," have with respect to " hyperspheres” of dimensions without bound? In what way might this infinite-dimensional constant be used in string theory? Most of my findings can be seen by following the links on Sloan's encyclopedia. From those links you will also come across a few references to more rigorous research done on that value's general form. If you endeavor to research this constant, I will try to help by answering any questions as to what I have already found in the past 9 years. last update-- Marvin Ray Burns 19:54, 15 April 2007 (UTC)
A recent observation about and definition of this constant can be found at http://www.marvinrayburns.com/what_is_mrb.mht [3]. I hope that, through the input of interested and knowledgeable people, this constant will qualify for an article on Wikipedia. Marvin Ray Burns ( talk) 01:45, 22 April 2009 (UTC)
http://en.wikipedia.org/wiki/Wikipedia:Reward_board#MRB_Constant -- Marvin Ray Burns 00:24, 17 April 2007 (UTC)
This page should be merged with Mathematical constants. Jaunt 16:50, 12 April 2007 (UTC)
It is obvious that this change needed to be made: http://en.wikipedia.org/?title=Mathematical_constant&diff=122317608&oldid=122257451
The old symbols were larger than the row height of the table. —-- Marvin Ray Burns 21:46, 12 April 2007 (UTC) Marburns ( talk • contribs) 21:33, 12 April 2007 (UTC).
is exact and not an approximate value. is approximate. Better is the Cartesian representation0.0+1.i. However, the last approximation uses i to define i. I believe it is best to put " exactly ." I'm going to post it and see if anyone has a better -- more accurate—way of displaying it.-- Marvin Ray Burns 01:55, 15 April 2007 (UTC)
Is the addition of complex number in the definition really appropriate? The only 'complex constant' I've head of is , because it's a 'unit'. Randomblue ( talk) 15:43, 11 December 2007 (UTC)
Hi fellow wikipedians! I've been checking all the constants in the list and verified the existence of each red one (except two) via Wolfram MathWorld (entries in that list, or found by searching that site).
There are however two constants which I fail to verify via internet searching: Hughes constant ("Sh") and Jacevicius constant ("J2").
Does anyone else know of these constants and can verify their existence, i.e. justify that they are present in the list? Otherwise, they might be subject for deletion...
Furthermore I find that the following uncategorized constants could be placed in the following fields of mathematics (as far as I understand from checking the articles and/or Wolfram MathWorld);
Any opinions on this? -- Dna-Dennis ( talk) 15:48, 3 February 2008 (UTC)
Why are all these constants small? Now I know "small" isn't really well defined, but why do constants tend to be close to 0 or 1. Not the most well defined question, but you know what I mean. Has there ever been any discussion in the literature about this? Brentt ( talk) 20:06, 6 May 2008 (UTC)
I just added a section about the decimal place similarity of irrational constants. More on this coming soon!
Quantum Anomaly ( talk) 04:48, 1 July 2008 (UTC)
Quantum Anomaly ( talk) 21:33, 8 July 2008 (UTC)
Removed text
It is interesting to note the frequent occurrence of irrational constants having the number nine in the 12th and/or 14th decimal places. [1] This pattern confirms a relationship between irrational constants and hints at the possibility of underlying self-similarity of a larger scale.
Pi: Phi: e: |
03.141592653589793238462643383279 01.618033988749894848204586834365 01.202056903159594285399738161511 02.236067977499789696409173668731 00.235711131719232931374143475359 00.764223653589220662990698731250 02.584981759579253217065893587383 02.718281828459045235360287471352 00.567143290409783872999968662210 |
Pi: Phi: |
03.141592653589793238462643383279 01.618033988749894848204586834365 01.414213562373095048801688724209 01.606695152415291763783301523190 01.202056903159594285399738161511 04.669201609102990671853203820466 02.502907875095892822283902873218 14.134725141734693790457251983562 00.114942044853296200701040157469 |
• In the numbers above, the last decimal is truncated, not rounded.
• 14.134... is known as "the imaginary part of the first nontrivial zero of the Riemann zeta function". It has been abbreviated in the table above.
The significance of nine in an irrational constant is also a theme of the Feynman point.
A new section titled "Equations" was added below "Calculation". I was going to remove the "Equations" and add the following to the bottom of "Calculation". However, the new section was reverted, a decision that I support (but failed to do myself due to lack of boldness). The expressions are quite cute, so here they are:
This result can be rearranged
-- Johnuniq ( talk) 04:13, 7 July 2008 (UTC)
I have twice four times now reverted an anonymous contributor who has added "Anton's constant" (value=6) to the table of mathematical constants. No source, no Google hits, no article, wikilinks are to
6 (number) and
rational number, so I am assuming this is complete nonsense.
Gandalf61 (
talk)
10:51, 15 October 2008 (UTC)
The table in this article says that the golden ratio is known to 3.14x10^9 places, while 5^0.5 is known to only 10^6 places. But the golden ratio is equal to (1+5^0.5)/2 so they must both be known to the same number of places. Which is right? Ehrenkater ( talk) 21:11, 22 November 2008 (UTC)
Looks pretty good to me... a big fat bold article in the middle of the mathematics vital articles is annoying. Leon math ( talk) 22:12, 4 January 2009 (UTC)
Shouldn't we include the approximate decimal values of the constants? I'm surprised no one's said anything about that. I hope I didn't miss anyone's comment... Leon math ( talk) 22:15, 4 January 2009 (UTC)
I think it would be nice to add one or two new rows for the computability / definability of each constant. What do you think? —Preceding unsigned comment added by 134.184.131.153 ( talk) 10:40, 6 September 2007 (UTC)
Should Chaitin's "constant" be here? It's not actually a real number until you've chosen a computational machine, and I'm not aware of any canonical choices for that. For any such choice, on the other hand, we can make some statements about Ω. For example, for any machine for which the string "0" is a program that simply terminates, Ω > 0.5. We might even know the first digit.
Prumpf 14:37, 14 Aug 2004 (UTC)
Is there any reason why and are listed as irrational rather than algebraic? Gkhan 16:45, Sep 7, 2004 (UTC)
Is the number 1 not a mathematical constant? It is used to define the set of natural numbers. -- Lambyuk 01:44, 13 May 2005 (UTC)
Err, 1 and 0 are not constants. They are numbers. In software development, for example, 0 is a literal, but A=0 would mean A is a constant representing number 0. Secondly, if we have 0 and 1, why not 2, 3 and 4? How about 0x0a? How about 20? It is also very interesting...
Similarly, i is the same as 1 but for the complex plane. Just a unit, nothing special. —Preceding unsigned comment added by 216.55.199.86 ( talk) 20:43, 14 February 2008 (UTC)
I've redone the table in (I hope) a better looking format. It is similar to format used on Table of mathematical symbols. Any comments? Paul August ☎
Some of the table rows need to be bigger. I would do it myself, but I don't want to mess it up. -Mihirgk
Right? (Are all constants that are irrational-but-not-transcendent algebraic?)
Is Mill's constant symbolised by theta (as in the table) or phi (as in it's seperate article)? -- Saboteur 01:11, 31 March 2006 (UTC)
Accoring to this article,D(1)=6/pi^2,not the HSM constant. It uses sigma for the HSM. We should change the symbol.
I just changed the symbol.
Is the Erdos-Borwein constant really algebraic? You should make something called I. It will mean "known to be irrational,may be algebraic or transcendental." That would be a good extra symbol.
Most precise does not equal most accurate. "Number of known digits" as used in this table means number of digits known to be correct, not number of digits that could be right. Fredrik Johansson 22:57, 6 September 2006 (UTC)
The article "
http://en.wikipedia.org/wiki/Cahen%27s_constant" give the following value :
0.64341054629...
What is the true value ?
cf [1]
Papy77
15:41, 1 February 2007 (UTC)
Is Mathematical constint a good redirect? Con stint 12:27, 27 February 2007 (UTC)
There are so many red links in the table. We should create some pages and remove the external links. Math Maniac 11:46, 1 March 2007 (UTC)
I would like to see if anyone can further expand upon my attempts of researching the following value. Sloan's A037077 ie. one of two real decimal expansions of 1^(1/1)-2^(1/2)+3^(1/3)... or a generalized sum to the divergent series. http://www.research.att.com/~njas/sequences/A037077 [2] This constant remains a mystery. For instance, before 1998 what was the computation-history of the value that is presently called the MRB Constant? What is the closed form expression (assuming it exists) for the value of this constant? What relation does this constant of infinite dimensional “ hypercubes," have with respect to " hyperspheres” of dimensions without bound? In what way might this infinite-dimensional constant be used in string theory? Most of my findings can be seen by following the links on Sloan's encyclopedia. From those links you will also come across a few references to more rigorous research done on that value's general form. If you endeavor to research this constant, I will try to help by answering any questions as to what I have already found in the past 9 years. last update-- Marvin Ray Burns 19:54, 15 April 2007 (UTC)
A recent observation about and definition of this constant can be found at http://www.marvinrayburns.com/what_is_mrb.mht [3]. I hope that, through the input of interested and knowledgeable people, this constant will qualify for an article on Wikipedia. Marvin Ray Burns ( talk) 01:45, 22 April 2009 (UTC)
http://en.wikipedia.org/wiki/Wikipedia:Reward_board#MRB_Constant -- Marvin Ray Burns 00:24, 17 April 2007 (UTC)
This page should be merged with Mathematical constants. Jaunt 16:50, 12 April 2007 (UTC)
It is obvious that this change needed to be made: http://en.wikipedia.org/?title=Mathematical_constant&diff=122317608&oldid=122257451
The old symbols were larger than the row height of the table. —-- Marvin Ray Burns 21:46, 12 April 2007 (UTC) Marburns ( talk • contribs) 21:33, 12 April 2007 (UTC).
is exact and not an approximate value. is approximate. Better is the Cartesian representation0.0+1.i. However, the last approximation uses i to define i. I believe it is best to put " exactly ." I'm going to post it and see if anyone has a better -- more accurate—way of displaying it.-- Marvin Ray Burns 01:55, 15 April 2007 (UTC)
Is the addition of complex number in the definition really appropriate? The only 'complex constant' I've head of is , because it's a 'unit'. Randomblue ( talk) 15:43, 11 December 2007 (UTC)
Hi fellow wikipedians! I've been checking all the constants in the list and verified the existence of each red one (except two) via Wolfram MathWorld (entries in that list, or found by searching that site).
There are however two constants which I fail to verify via internet searching: Hughes constant ("Sh") and Jacevicius constant ("J2").
Does anyone else know of these constants and can verify their existence, i.e. justify that they are present in the list? Otherwise, they might be subject for deletion...
Furthermore I find that the following uncategorized constants could be placed in the following fields of mathematics (as far as I understand from checking the articles and/or Wolfram MathWorld);
Any opinions on this? -- Dna-Dennis ( talk) 15:48, 3 February 2008 (UTC)
Why are all these constants small? Now I know "small" isn't really well defined, but why do constants tend to be close to 0 or 1. Not the most well defined question, but you know what I mean. Has there ever been any discussion in the literature about this? Brentt ( talk) 20:06, 6 May 2008 (UTC)
I just added a section about the decimal place similarity of irrational constants. More on this coming soon!
Quantum Anomaly ( talk) 04:48, 1 July 2008 (UTC)
Quantum Anomaly ( talk) 21:33, 8 July 2008 (UTC)
Removed text
It is interesting to note the frequent occurrence of irrational constants having the number nine in the 12th and/or 14th decimal places. [1] This pattern confirms a relationship between irrational constants and hints at the possibility of underlying self-similarity of a larger scale.
Pi: Phi: e: |
03.141592653589793238462643383279 01.618033988749894848204586834365 01.202056903159594285399738161511 02.236067977499789696409173668731 00.235711131719232931374143475359 00.764223653589220662990698731250 02.584981759579253217065893587383 02.718281828459045235360287471352 00.567143290409783872999968662210 |
Pi: Phi: |
03.141592653589793238462643383279 01.618033988749894848204586834365 01.414213562373095048801688724209 01.606695152415291763783301523190 01.202056903159594285399738161511 04.669201609102990671853203820466 02.502907875095892822283902873218 14.134725141734693790457251983562 00.114942044853296200701040157469 |
• In the numbers above, the last decimal is truncated, not rounded.
• 14.134... is known as "the imaginary part of the first nontrivial zero of the Riemann zeta function". It has been abbreviated in the table above.
The significance of nine in an irrational constant is also a theme of the Feynman point.
A new section titled "Equations" was added below "Calculation". I was going to remove the "Equations" and add the following to the bottom of "Calculation". However, the new section was reverted, a decision that I support (but failed to do myself due to lack of boldness). The expressions are quite cute, so here they are:
This result can be rearranged
-- Johnuniq ( talk) 04:13, 7 July 2008 (UTC)
I have twice four times now reverted an anonymous contributor who has added "Anton's constant" (value=6) to the table of mathematical constants. No source, no Google hits, no article, wikilinks are to
6 (number) and
rational number, so I am assuming this is complete nonsense.
Gandalf61 (
talk)
10:51, 15 October 2008 (UTC)
The table in this article says that the golden ratio is known to 3.14x10^9 places, while 5^0.5 is known to only 10^6 places. But the golden ratio is equal to (1+5^0.5)/2 so they must both be known to the same number of places. Which is right? Ehrenkater ( talk) 21:11, 22 November 2008 (UTC)
Looks pretty good to me... a big fat bold article in the middle of the mathematics vital articles is annoying. Leon math ( talk) 22:12, 4 January 2009 (UTC)
Shouldn't we include the approximate decimal values of the constants? I'm surprised no one's said anything about that. I hope I didn't miss anyone's comment... Leon math ( talk) 22:15, 4 January 2009 (UTC)