Re: [OT] xy == yx

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From	Peter Pearson <pkpearson@nowhere.invalid>
Newsgroups	comp.lang.python
Subject	Re: [OT] xy == yx
Date	10 Jan 2015 16:57:14 GMT
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On Fri, 09 Jan 2015 23:41:15 +0200, Marko Rauhamaa <marko@pacujo.net> wrote:
> Peter Pearson <pkpearson@nowhere.invalid>:
>
>> If you've never looked at the set of reals (x,y) satisfying x**y ==
>> y**x, it's worth a visit.
>
> Thanks, it was. The graph's something like this:
[snip]
>
> Where can I read more on the topic?

Sorry, I don't know.  One Phil Rust steered me to this problem in high
school (c. 1964), and I never got much traction on it until Prof. Alfred
Roch at EPFL pointed out (c. 1981) that it's revealing to think of
horizontal lines intersecting the graph of ln(x)/x.

If you like this sort of thing, here's another cute function that
the same Phil Rust called to my attention:
http://webpages.charter.net/curryfans/peter/XtoTheXtoTheX/ode_to_e.html

-- 
To email me, substitute nowhere->runbox, invalid->com.

Thread

Re: Decimals and other numbers Devin Jeanpierre <jeanpierreda@gmail.com> - 2015-01-08 19:02 -0800
  Re: Decimals and other numbers Marko Rauhamaa <marko@pacujo.net> - 2015-01-09 09:28 +0200
    Re: Decimals and other numbers Chris Angelico <rosuav@gmail.com> - 2015-01-09 18:37 +1100
      Re: Decimals and other numbers Marko Rauhamaa <marko@pacujo.net> - 2015-01-09 11:31 +0200
    Re: Decimals and other numbers Dave Angel <davea@davea.name> - 2015-01-09 02:49 -0500
    Re: Decimals and other numbers Devin Jeanpierre <jeanpierreda@gmail.com> - 2015-01-09 00:51 -0800
      Re: Decimals and other numbers Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2015-01-09 11:07 +0200
        [OT] x**y == y**x Peter Pearson <pkpearson@nowhere.invalid> - 2015-01-09 17:46 +0000
          Re: [OT] x**y == y**x Marko Rauhamaa <marko@pacujo.net> - 2015-01-09 23:41 +0200
            Re: [OT] x**y == y**x Peter Pearson <pkpearson@nowhere.invalid> - 2015-01-10 16:57 +0000
  Re: Decimals and other numbers Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-01-09 19:49 +1100
    Re: Decimals and other numbers Devin Jeanpierre <jeanpierreda@gmail.com> - 2015-01-09 00:58 -0800
      Re: Decimals and other numbers Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-01-09 21:20 +1100
        Re: Decimals and other numbers Chris Angelico <rosuav@gmail.com> - 2015-01-09 21:39 +1100
          Re: Decimals and other numbers Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-01-09 23:24 +1100
            Re: Decimals and other numbers Chris Angelico <rosuav@gmail.com> - 2015-01-09 23:34 +1100
        Re: Decimals and other numbers Devin Jeanpierre <jeanpierreda@gmail.com> - 2015-01-09 17:25 -0800
        Re: Decimals and other numbers Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2015-01-10 16:08 +1300
    Re: Decimals and other numbers Devin Jeanpierre <jeanpierreda@gmail.com> - 2015-01-09 01:11 -0800
    Re: Decimals and other numbers Marko Rauhamaa <marko@pacujo.net> - 2015-01-09 11:34 +0200
      Re: Decimals and other numbers Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-01-09 22:03 +1100
    Re: Decimals and other numbers Marko Rauhamaa <marko@pacujo.net> - 2015-01-09 11:44 +0200
    Re: Decimals and other numbers Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2015-01-10 16:05 +1300
      Re: Decimals and other numbers Devin Jeanpierre <jeanpierreda@gmail.com> - 2015-01-09 19:57 -0800

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