# Are 'pi' and 'e' related? **URL:** \ **Category:** Factual Questions\ **Created:** [June 26, 2001, 1:42am UTC](https://boards.straightdope.com/t/are-pi-and-e-related/70155 "2001-06-26T01:42:59Z")\ **Posts on this page:** 11\ **Page:** 2
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [July 17, 2015, 6:20pm UTC](https://boards.straightdope.com/t/are-pi-and-e-related/70155/21 "2015-07-17T18:20:07Z")
[Also relevant xkcd](https://xkcd.com/217/) ---
**Author:** ![Isilder](https://avatars.discourse-cdn.com/v4/letter/i/cc9497/32.png) [@Isilder](https://boards.straightdope.com/u/Isilder)\ **Post date:** [July 17, 2015, 9:56pm UTC](https://boards.straightdope.com/t/are-pi-and-e-related/70155/22 "2015-07-17T21:56:57Z")
> [@zekrommaster11](#): > > One amazing relation that I found out: ln(pi)=1/logbasepi(e) ~~ 1.144729… I found this out using desmos and tested it out by graphing, it works. 🙂 Napiers bones, the slide rule… they work because addition and substraction of logs is multiplication and division of the subjects … as in X/Y = z ^ ( log z X - log z Y ) … for any z ---
**Author:** ![KarlGauss](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/karlgauss/32/3713_2.png) [@KarlGauss](https://boards.straightdope.com/u/KarlGauss)\ **Post date:** [July 18, 2015, 1:33am UTC](https://boards.straightdope.com/t/are-pi-and-e-related/70155/23 "2015-07-18T01:33:57Z")
> [@zekrommaster11](#): > > One amazing relation that I found out: ln(pi)=1/logbasepi(e) ~~ 1.144729… I found this out using desmos and tested it out by graphing, it works. 🙂 That’s nothing. Not when you consider the fact that 6π[sup]5[/sup] = [proton to electron mass ratio](https://en.wikipedia.org/wiki/Proton-to-electron_mass_ratio) 😉 ---
**Author:** ![standingwave](https://avatars.discourse-cdn.com/v4/letter/s/9de0a6/32.png) [@standingwave](https://boards.straightdope.com/u/standingwave)\ **Post date:** [July 18, 2015, 3:17am UTC](https://boards.straightdope.com/t/are-pi-and-e-related/70155/24 "2015-07-18T03:17:46Z")
My favorite: **pi^4 + pi^5 = e^6** ---
**Author:** ![KarlGauss](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/karlgauss/32/3713_2.png) [@KarlGauss](https://boards.straightdope.com/u/KarlGauss)\ **Post date:** [July 18, 2015, 3:36am UTC](https://boards.straightdope.com/t/are-pi-and-e-related/70155/25 "2015-07-18T03:36:21Z")
> [@standingwave](#): > > My favorite: > > **pi^4 + pi^5 = e^6** Never saw that before. Excellent. Thanks! ---
**Author:** ![John\_Mace](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/john_mace/32/185_2.png) [@John\_Mace](https://boards.straightdope.com/u/John_Mace)\ **Post date:** [July 18, 2015, 3:42am UTC](https://boards.straightdope.com/t/are-pi-and-e-related/70155/26 "2015-07-18T03:42:52Z")
> [@KarlGauss](#): > > That’s nothing. Not when you consider the fact that 6π[sup]5[/sup] = [proton to electron mass ratio](https://en.wikipedia.org/wiki/Proton-to-electron_mass_ratio) > > 😉 The fact that pi would show up in something spherical is simply geometry. Nothing surprising at all. ---
**Author:** ![Hellestal](https://avatars.discourse-cdn.com/v4/letter/h/3ab097/32.png) [@Hellestal](https://boards.straightdope.com/u/Hellestal)\ **Post date:** [July 18, 2015, 3:49am UTC](https://boards.straightdope.com/t/are-pi-and-e-related/70155/27 "2015-07-18T03:49:59Z")
> [@standingwave](#): > > My favorite: > > **pi^4 + pi^5 = e^6** Pretty sure that’s an approximation, not a perfect equation. ---
**Author:** ![KarlGauss](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/karlgauss/32/3713_2.png) [@KarlGauss](https://boards.straightdope.com/u/KarlGauss)\ **Post date:** [July 18, 2015, 3:57am UTC](https://boards.straightdope.com/t/are-pi-and-e-related/70155/28 "2015-07-18T03:57:43Z")
> [@John\_Mace](#): > > The fact that pi would show up in something spherical is simply geometry. Nothing surprising at all. [Quote=Hellestal] Originally Posted by standingwave My favorite: **pi^4 + pi^5 = e^6** Pretty sure that’s an approximation, not a perfect equation. [/quote] Whoosh. And whoosh. Unless I’m being whooshed (twice). ---
**Author:** ![standingwave](https://avatars.discourse-cdn.com/v4/letter/s/9de0a6/32.png) [@standingwave](https://boards.straightdope.com/u/standingwave)\ **Post date:** [July 18, 2015, 4:06am UTC](https://boards.straightdope.com/t/are-pi-and-e-related/70155/29 "2015-07-18T04:06:30Z")
> [@Hellestal](#): > > Pretty sure that’s an approximation, not a perfect equation. True. A very close approximation to be sure, like the second xkcd toon posted above. Close enough to drive people nuts. ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [July 18, 2015, 8:53am UTC](https://boards.straightdope.com/t/are-pi-and-e-related/70155/30 "2015-07-18T08:53:02Z")
It would have been less misleading to write π[sup]4[/sup] + π[sup]5[/sup] = e[sup]5.999999956…[/sup]Wikipedia has a nice page of such close approximations, but I can’t find that page right now. Is this one on it? Anyway, it does seem remarkable! Another famous approximation is e[sup]π √163[/sup] = 262537412640768743.999999999999… This is related to some number theory; how about π[sup]4[/sup] + π[sup]5[/sup] = e[sup]5.999999956…[/sup] ? ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [July 18, 2015, 9:23am UTC](https://boards.straightdope.com/t/are-pi-and-e-related/70155/31 "2015-07-18T09:23:24Z")
> [@septimus](#): > > Another famous approximation is e[sup]π √163[/sup] = 262537412640768743.999999999999… Oops. I should have added a few more digits e[sup]π √163[/sup] = 262537412640768743.999999999999250… to emphasize that the infamous .99999999999999999999999999999… (which _is_ an integer) was not intended. 🙂 [Previous page](https://boards.straightdope.com/t/are-pi-and-e-related/70155.md?page=1)