Talk:E (mathematical constant)/Archive 2

message: The last infinite series listed in this article is
:e =  \frac{-12}{\pi^2} \left [ \sum_{k=0}^\infty \frac{1}{k^2} \ \cos \left ( \frac{9}{k\pi+\sqrt{k^2\pi^2-9}} \right ) \right ]^{-1/3} .
But for k=0 we have division by zero (and also the square root of a negative number). I think the sum should start from k=1. Can anyone confirm? Eric119 04:08, 2 January 2006 (UTC)
replies: text: Hey thanks for being on the lookout, Eric; the sum does indeed start at 1 (I contributed this sum) and I fixed it.--Hypergeometric2F1[a,b,c,x] 07:11, 2 January 2006 (UTC)
thread_title:  The last infinite series 

message: A friend of mine wrote a little computer program that can make an article title begin with a lower case letter. Is anyone interested in changing the title of this article from  E (mathematical constant) to e (mathematical constant)? Uncle Ed 13:16, 10 January 2006 (UTC)
replies: text: How ugly are the hacks involved? MediaWiki 1.6 will be case-insensitive and nativly support names which start with a lower case letter. —Ruud 13:20, 10 January 2006 (UTC)
replies: text: It probably involves using some of the "fullwidth" letters in Unicode. æle ✆ 20:35, 17 January 2006 (UTC)
replies: text:  I don't think it is worth the trouble. Oleg Alexandrov (talk) 01:37, 18 January 2006 (UTC)
thread_title: Title in lower case

message: ... would generally include "0" and "1".  As per the "famous five" of Euler's identity, indeed.  I won't edit this directly in case anyone's upset, y'all just having had a poll, n'stuff. :)  Alai 08:54, 30 January 2006 (UTC)
replies: text: I agree that they are important. I am not sure it is worth the trouble adding them to this article, as it is primarily about e. But, whatever. :) Oleg Alexandrov (talk) 04:56, 31 January 2006 (UTC)
replies: text: I make the point as at present, it's a little counter-intuitive to the non-mathshead, as we start off with a comparison with the "unusual" numbers pi and i, which may be puzzling to people not clear what the importance of those actually is.  Juxtaposing with the more familiar numbers makes the point more strongly, I feel.  Alai 08:26, 31 January 2006 (UTC)
replies: text: I am persuaded by your argument and Oleg's lack of objection.  -lethe talk [ +] 09:41, 31 January 2006 (UTC)

text: So the 1 that appears in Euler's identity seems to have more to do with multiplicative identities than generators of integers to me.  e0 is e times itself no times, which must be the multiplicative identity.  The function ex does have period 2iπ, so the one there in Euler's identity is a multiplicative identity.  I think if you viewed the exponent as 1*iπ, then the 1 in the exponent would be the additive generator of the integers, but that's suppressed.  Now, as for whether mentioning identities is good for the intro, well if we think they're important, we have to say why.  We already say that i is the imaginary unit.  We should say what 0 and 1 are as well.  I mean, everyone knows the numbers 0 and 1, but might not have the foggiest why someone should consider them as important as π and e.  If I knew a 2 word description of why π was important, I would include that as well. -lethe talk [ +] 19:35, 31 January 2006 (UTC)
replies: text: Circumference-to-diameter ratio? Paul August ☎ 23:18, 31 January 2006 (UTC)
replies: text:  That's cheating :) —Ruud 23:22, 31 January 2006 (UTC)
replies: text:  Well, it's half the rotational identity, or "semicircular period", or "trigonometric period"? How about "pandisciplinary constant"? ... Well, I suppose that applies to all of them. Damn, I give up. Confusing Manifestation 09:15, 1 February 2006 (UTC)
replies: text: I'm going to try out Paul's suggestion.  I think it's a bit too bulky for the sentence, but you guys take a look and tell me what you think.  I'm counting on you, R Koot, to not like it. -lethe talk [ +] 09:41, 1 February 2006 (UTC)
replies: text:  Given that nobody can come up with something better, it will have to do. —Ruud 12:24, 1 February 2006 (UTC)
thread_title:  Most important numbers... 

message: There are a number of more complicated concepts in math that have been explained in laymen's terms.  The problem with the e discussion is that no attempt is made to explain what "natural" means.  It is either arrogant or wrong to say that no one si or will be interested in e if they are not concerned with pure math, physics, etc.
("Also, questions are more likely to be seen when they get proper headings and go to the bottom of the page, which this did not. -lethe talk [ +] 19:53, 3 February 2006 (UTC)
replies: text: perhaps so, but the thread is lost this way.) Kdammers 11:21, 6 February 2006 (UTC)

text: Is wikipedia suppost to teach people math?  It is your responsibility to learn e in the context of a higher math class, or in a historical setting such as the book E: Story of a Number.--Hypergeometric2F1[a,b,c,x] 19:27, 6 February 2006 (UTC)
replies: text: No, you are wrong.  Wik is an encyclopedia, not a dictionary or a discussion board.  Its obligation is to provide clear explanations (and many if not most Wikians seem to think these should be for lay-people, since there are - especially in math entries - statements llike "We don't need togo into the technical stuff since experts have their own journals and books and won't be looking here").  Kdammers 01:28, 7 February 2006 (UTC)
replies: text: Hypergeometric is not wrong.  Wikipedia is not a textbook or a classroom (but see wikibooks and wikiversity).  We are a reference work.  You are certainly wrong that experts do not use this encyclopedia.  Now if someone has some constructive comments, I'm sure we'd be happy to address them.  But complaining and making broad generalizations about the nature of the pedia and what experts do with their time is helping nothing.  -lethe talk [ +] 03:58, 7 February 2006 (UTC)
replies: text: Are you guys replying to me?--Hypergeometric2F1[a,b,c,x] 05:16, 7 February 2006 (UTC)
replies: text: Well, I was replying to Kdammers, but I was talking about you, but for some reason I called you linas.  That was really weird, I'm sorry for the mixup! (I fix it). -lethe talk [ +] 21:06, 7 February 2006 (UTC)

text: PS Renaming the picture to something like E-math_constant.png from E-derivative.svg might be good also. :) Oleg Alexandrov (talk) 04:02, 7 February 2006 (UTC)
replies: text:  Sorry :) it was a crude sketch in mathemtica so see if people liked it, still have to learn how gnuplot works. —Ruud 14:58, 7 February 2006 (UTC)

text: E; the unique number such that 14242+e^(-23) = 14242 +e^(-23) --Hypergeometric2F1[a,b,c,x] 05:21, 7 February 2006 (UTC)
replies: text:  So e = 4 and e = 3 and ..? That doesn't sound very unique to me. —Ruud 15:04, 7 February 2006 (UTC)
replies: text: I was being sarcastic...n/m lol..--Hypergeometric2F1[a,b,c,x] 21:17, 7 February 2006 (UTC)
thread_title:  Clearly defining e 

message: I don't like the current ℮ (mathematical constant) title. I would think moving it back to E (mathematical constant) would be better. Comments? Oleg Alexandrov (talk) 23:31, 26 February 2006 (UTC)
replies: text: Agreed. ℮ is the "estimated symbol". It has nothing to do with the constant e. I have moved the article back, accordingly. Nohat 00:10, 27 February 2006 (UTC)
thread_title:  The move 

message: In my oppinion, the natural occurences of e section of the article sould be creaded and expanded. What are your oppinions on this topic?--BorisFromStockdale 21:09, 9 March 2006 (UTC)
thread_title: Natural occurences of e

message: This page was moved to mathematical constant e.  I don't support such a move, so I've moved it back to e (mathematical constant).  If and when a consensus should arise for another name, then I won't oppose. -lethe talk [ +] 09:04, 15 March 2006 (UTC)
replies: text: I agree; the name Mathematical constant e is also bad-sounding. Oleg Alexandrov (talk) 19:05, 15 March 2006 (UTC)
thread_title:  move to [[Mathematical constant e]] 

message: Someone named Hiiiiiiii recently added one more digit.  The text claimed 29 digits, so adding another made the text incorrect.  I fixed the text, and clarified that it's truncating, not rounding (though maybe we should prefer to round up?).  Furthermore, I added the digit back, becaues I seem to remember my old fashioned tables of numbers format things in blocks of five digits aligned to the decimal point.  I could be misremembering though. -lethe talk [ +] 18:08, 7 April 2006 (UTC)
thread_title:  one more digit 

message: The page was moved a second time to ℮ (mathematical constant).  I guess there is some support for the idea, but I'm sure also some opposition.  I've moved back. -lethe talk [ +] 20:31, 11 April 2006 (UTC)
replies: text: My unicode browser tells me that ℮ is the "estimated symbol".  Can someone defend the stance that it denotes the natural logarithm base?  -lethe talk [ +] 20:34, 11 April 2006 (UTC)
replies: text: If the sole reason is that this symbol looks like a miniscule e, then I find this wholly unconvincing.  If that were a convincing reason, I would prefer the unicode ℯ, but it's not convincing, so I don't. -lethe talk [ +] 20:36, 11 April 2006 (UTC)

text: From the edit summary, I infer that this semi-clever (heh) idea originated on the Hebrew wikipedia.  I notice that the Italian article also uses it, but no other language does. -lethe talk [ +] 21:18, 12 April 2006 (UTC)
thread_title:  page move 

message: Isn't the curvature of e used in erecting structures? I remember learning that a parabolic shape wouldn't be as good as an e shape. Anyone have any information on this? 71.250.59.37 20:22, 3 May 2006 (UTC)
replies: text: The inverted catenary \frac{e^{-x}+e^{x}}{2} is one of the most stable structures if that is what you are thinking of.  The St Louis arch is an inverted centenary. --Hypergeometric2F1(a,b,c,x) 17:24, 13 December 2006 (UTC)
thread_title:  e in the real world 

message: Is there any good reason why the horizontal and vertical axes of the :Image:E-ruud.png are not drawn to the same scale? Evercat 20:12, 9 June 2006 (UTC)
replies: text: More effort, I was lazy. —Ruud 20:31, 10 June 2006 (UTC)
thread_title:  The image 

message: The text cites A005131 as the simple continued fraction of e, but OEIS:A003417 says it is. The latter looks more reasonable to me. Then the question is, what is OEIS:A005131?Lee S. Svoboda tɑk 22:11, 26 August 2006 (UTC)
replies: text: The article is wrong.  Both are continued fraction expansions of e; the only difference is that one begins "2,..." and the other begins "1,0,1,...".  These have the same value.  (In general, any continued fraction expansion that contains "...m, 0, n, ..." is equal to one that contains "...m+n, ..." at the same position.)  But only the first of these is a simple continued fraction expansion, because simple continued fractions are required to have positive terms.  I will correct the article.  -- Dominus 14:06, 27 August 2006 (UTC)
replies: text:  Thank you. Lee S. Svoboda tɑk 17:18, 30 August 2006 (UTC)

text: Thank you, Glenn L. I am amazed – someone else actually cares about these things!  DavidCBryant 12:19, 17 January 2007 (UTC)
thread_title:  Continued fraction 

message: I added a third generalized continued fraction that converges far more quickly than the first two. It corresponds to the series
1/1, 3/1, 19/7, 193/71, 2721/1001, ...
Each convergent adds 2-3 decimal digits of precision to its predcessor. 
I also added a general formula for e^(2m/n) for |m|,n = 1,2,3,...; however, convergence slows as |m| increases in value. When m=1 and n=2 you get the formula for e.
Glenn L
:Thank you, Glenn L. I am amazed – someone else actually cares about these things!  DavidCBryant 12:19, 17 January 2007 (UTC)
thread_title: ========

message: The graph comparing f(x)=e^x to f'(x) is nice, but a little confusing, if only because x=.7 (whatever it is, don't have calculator handy), which gives f(x) = 2.  Which is nice, but not entirely evident unless you know to look for it.  Perhaps showing x=1 would help, and showing the equation "e^(.7whatever) = 2, which is the slope at that point, and e^1 = 1, which is the slope there."  Perhaps even more explicitly labelling the slope of 2 would help (either with a direct label, or an old middleschool "rise over run" triangle, showing that it goes up 2 for every 1 over).  And, I may be splitting hairs, but it seems like the line for e^x should be bolded, or that the f' line should not be given equal weight.  I say this just because it is the first (and only) graph on the page, so it is doing double duty: showing the function e^x (very important) and showing that that derivative of e^x equals e^x (important, but less important than showing that function itself). Sir Isaac Lime 20:13, 19 September 2006 (UTC)
thread_title: Graph

message: I think that a picture showing the tangent line at 1, instead of 2 would ilustrate the point much more clearly... a slope of one is easier to see. 160.39.168.58 04:25, 11 December 2006 (UTC)
thread_title:  picture 

message: Does that mean the additive identity is 0 and the multiplicative identity is 1, or does it mean "the [actions] of addition and multiplication and the numbers 0 and 1"? Could someone please clarify this on the page. --Hugh7 08:44, 24 January 2007 (UTC)
thread_title: "alongside the additive and multiplicative identities 0 and 1"

message: Right now it's listed as the sum of (1/n!) from 0 to infinity; this doesn't seem to be right because 1/0! is 1, or am I mistaken? (I had learned before that 0! is a special case equal to 1) Since 1/0! + 1/1! is already 2, the next few numbers (2 through 6, I think) make the value pass 1... could somebody clear this up for me? Robinson0120 02:04, 28 January 2007 (UTC)
replies: text: No, 1/n! gets smaller very fast.  Look at the first few terms: 1 + 1 + 1/2 + 1/6 + 1/24 + 1/120 + 1/720... that's the 0 through 6 terms, which sum to 2.71805...; the first 3 decimal places are correct, e converges quite fast! –EdC 02:25, 28 January 2007 (UTC)
thread_title: A Possible Problem with the Definition of e

message: Ruud's graph showing the tangent to e^x at x=0 was replaced by a nice SVG graph with a tangent drawn at a different place, and the simple definition that e is the unique number such that the slope of the tangent to e^x at 0 is 1 was replaced by the much more scary-sounding (equivalent but over-specified) definition that e is the unique number such that the slope of the tangent to e^x is e^x for all x.  Why?  Can we modify the SVG and the definition back to the much simpler version, such that the graph actually illustrates the condition?  We could also draw some light curves for 2^x and 4^x just to illustrate that they have different slope, not 1, at x=0. Dicklyon 03:17, 28 January 2007 (UTC)
replies: text: Yeah, like it. –EdC 15:07, 28 January 2007 (UTC)
replies: text:  I think it's a good idea, Dick. I'm not so sure about the other curves, like 4x, though. They don't show up very well on your prototype. Maybe just one light curve, like 1.1x, would make the point more clearly. Oh – I searched through the history, and the old picture you referred to got wiped out of this article on 21 Aug, 2006, by an anon.  DavidCBryant 16:09, 28 January 2007 (UTC)
replies: text: I updated it with bolder dashed and dotted curves that show up better and don't confuse with other.  Does that work better for you?  I think these curves that obviously go through (1,2) and (1,4) will make the point better than curves further away. Dicklyon 17:27, 28 January 2007 (UTC)
replies: text: That looks good to me, Dick.  DavidCBryant 18:53, 28 January 2007 (UTC)
thread_title: Graph and definition

message: I know very little about mathmatical concepts such as this, so I don't feel very comfortable editing the article, but it's my understanding that e is an irrational number, and this doesn't come across very clearly in the article. Does anyone object to this being mentioned in the opening paragraph? I think it would help expalin why the number is not shown in its entirety. -R. fiend 18:44, 10 February 2007 (UTC)
replies: text: Done.  Transcendental, too. Dicklyon 19:10, 10 February 2007 (UTC)
thread_title: irrational number

message: User:Hypergeometric2F1(a,b,c,x) put in a formula back on 21 December 2005 that had previously been repeatedly inserted by a user who called it "Keller's Expression", presumably after himself.  This self-promotion had been removed several times before.  Today I removed it yet again.  -- Dominus 16:33, 15 February 2007 (UTC)
thread_title:  Return of "Keller's Expression"