[OT] x**y == y**x

[Peter Pearson]

On Fri, 09 Jan 2015 23:41:15 +0200, Marko Rauhamaa <marko at pacujo.net> wrote:
> Peter Pearson <pkpearson at 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

-- 
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