Yes! USENET archives! The "new Google Groups" entirely fails to work, because its search engine has been dumbed down too much. But with the old Google Groups, I found the following, from 1989. That pushes it back 9 years earlier than Weisstein/CRC. "Doug Ingram" was closest to the source, but "it warn't him neether..." ---8<--snip-here---- Newsgroups: sci.math From: do...@utastro.UUCP (Doug Ingram) Date: 5 Jul 89 15:59:59 GMT Local: Wed, Jul 5 1989 11:59 am Subject: Relation between pi and e? A couple of days ago, someone posted this in their .sig file: 4 5 6 Pi + Pi = e Strange enough to be true????? Well, it comes close on my calculator, but it may be off due to roundoff error. Is this a coincidence, or can someone offer proof of this relation, maybe using e^(i*phi) = cos(phi) + i*sin(phi)? -------------------- Doug Ingram (dougi) do...@astro.as.utexas.edu do...@utastro.uucp {charm,ut-sally,emx,noao}!utastro!dougi dougi%astro.as.utexas.edu@{CUNYVM.CUNY.EDU,WISCVM.WISC.EDU} 'Airline food is of the highest quality, and critics who think otherwise are not objective at all...pardon me while I go make lasagne from used bus seats.' - Airline Food Employee -- Dave Barry Newsgroups: sci.math From: dkei...@Gang-of-Four.Stanford.EDU (Dave Eisen) Date: 6 Jul 89 10:31:08 GMT Local: Thurs, Jul 6 1989 6:31 am Subject: Re: Relation between pi and e?
4 5 6 Pi + Pi = e Strange enough to be true?????
pi**4 + pi**5 doesn't equal e**6, and if we are given the values of e and pi to about 13 or more digits we can prove it.
This is sci.math? Then how come I've seen a half dozen computations that show $$ \pi^4 + \pi^5 \ne e^6 $$ by numerical coincidence. Don't all mathematicians know from birth that $\pi$ and $e$ are algebraically independent? I'm not a number theorist so I don't know the reasoning behind it and I don't know the references that well. Still, this is the kind of fact that smells like it has to be discussed in Hardy and Wright. Experts?? Dave Eisen dkei...@Gang-of-Four.Stanford.EDU (415)723-2963 "It is poignant but fundamental that the flag protects those who hold it in contempt." --- Associate Justice Anthony Kennedy Newsgroups: sci.math From: mo...@hpcupt1.HP.COM (John Mount) Date: 6 Jul 89 00:24:05 GMT Local: Wed, Jul 5 1989 8:24 pm Subject: Re: Relation between pi and e? / hpcupt1:sci.math / do...@utastro.UUCP (Doug Ingram) / 8:59 am Jul 5, 1989 /
A couple of days ago, someone posted this in their .sig file: 4 5 6 Pi + Pi = e Strange enough to be true?????
pi**4 + pi**5 doesn't equal e**6, and if we are given the values of e and pi to about 13 or more digits we can prove it. we put some rational bounds on e and pi and then do infinite precision arithmetic (actually we do 99 digit precsion using bc calculator but since we have only about 12 digits in the numbers and deal with only 6th powers we need only 6x12 = 72 digits to acheive calculations that have *no* roundoff error) on these numbers to get bounds on the results (left one rounded down right one rounded up). If pi to about 13 digits after the decimal is: 3.14159265358979323 and e to a lot of figures is: 2.7182818284590452 (from math.h so if wrong not my fault) we know 3.14159265358 <= p <= 3.14159265359 therefore 403.428775 <= pi**4 + pi**5 <= 403.428776 and 2.7182818284 <= e <= 2.7182818285 therfore 403.428793 <= e**6 <= 403.428794 and we see that these two intervals do not overlap so the two quantities are not equal. John Mount ----8<--snippy-be-done---- - Robert Munafo On 2012-04-28, David Wilson <davidwwilson@comcast.net> wrote:
I first started working on the OEIS back in 1997 (My earliest contributions were in the A02xxxx range). I'm pretty sure I knew about the identity at that time, and I guess this clinches it.
But still, it came from an email signature in a Usenet group, so perhaps we could find the originator in the Usenet archives, if there is such a thing.
On 4/28/2012 11:24 AM, Robert Munafo wrote:
David, you must have told Eric Weisstein about it at least as early as 1998.
I just checked my copy of "The CRC concise encyclopedia of mathematics", dated 1998 (CRC Press, ix + 1969 pages, LC number 98-22385). It includes the near-identity and credits "D. Wilson". It is on page 33, right column, equation (7) near the bottom.
-- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com
This message gives me pause, though. The poster makes it sound as if pi^4 + pi^5 = e^6 was already circulating and debunked several times over, only 3 days after Frederiksen's post. Not that this disproves that Frederiksen was the discoverer, but it raises the possibility that Frederiksen was simply parroting an already circulating curiosity (which might also explain why Frederiksen never claimed authorship or apparently said anything more about the subject after this thread).
Newsgroups: sci.math From: dkei...@Gang-of-Four.Stanford.EDU (Dave Eisen) Date: 6 Jul 89 10:31:08 GMT Local: Thurs, Jul 6 1989 6:31 am Subject: Re: Relation between pi and e?
4 5 6 Pi + Pi = e Strange enough to be true?????
pi**4 + pi**5 doesn't equal e**6, and if we are given the values of e and pi to about 13 or more digits we can prove it.
This is sci.math? Then how come I've seen a half dozen computations that show $$ \pi^4 + \pi^5 \ne e^6 $$ by numerical coincidence. Don't all mathematicians know from birth that $\pi$ and $e$ are algebraically independent? I'm not a number theorist so I don't know the reasoning behind it and I don't know the references that well. Still, this is the kind of fact that smells like it has to be discussed in Hardy and Wright. Experts?? Dave Eisen dkei...@Gang-of-Four.Stanford.EDU (415)723-2963 "It is poignant but fundamental that the flag protects those who hold it in contempt." --- Associate Justice Anthony Kennedy
If you computed the circumference of a circle using 355/113 for pi, and were 1 inch off from the true circumference, the circle would enclose the state of Connecticut.
On 2012-04-29, David Wilson <davidwwilson@comcast.net> wrote:
This message gives me pause, though. The poster makes it sound as if pi^4 + pi^5 = e^6 was already circulating and debunked several times over, only 3 days after Frederiksen's post. Not that this disproves that Frederiksen was the discoverer, but it raises the possibility that Frederiksen was simply parroting an already circulating curiosity (which might also explain why Frederiksen never claimed authorship or apparently said anything more about the subject after this thread).
Yes, I agree. Just having those couple messages by Soren Frederiksen isn't enough to convince me, but it's a good lead. I used the good version of Google Groups to search for all messages with that name, and this is the first: http://groups.google.com/group/rec.arts.sf-lovers/msg/faf9e99459199126 Notice that he starts the message with "This is the first time I'm posting, so hopefully this will work properly ...", so it's his first USENET message. Note also the lack of the equation in his sig. Messages posted slightly later, like this one: http://groups.google.com/group/rec.arts.sf-lovers/msg/028a0de3a609007e also lack the formula. They're talking about digit patterns, in the context of Sagan's book "Contact" (on which the later movie was based), so the conversation touches on statistics of the digits of pi and what would constitute a "message". Within that context the pi^4+pi^5=e^6 formula has a mystical "put there by the divine creator" appeal to it, similar to what they were talking about (and which makes more sense if you've read the book. The Pi sub-plot was omitted from the movie.) To perform searches, use http://groups.google.com/advanced_search?q=& and note that it won't work if you attempt to sort by date. -- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com
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