Parametric Graph of x^y=y^x

Christian Goldbach found this parametric equation for the non-trivial branch of [math]x^y=y^x[/math] in 1728 (the trivial branch is just y=x). As t goes to plus or minus infinity, the points converge to (e,e). The values where x<2 or y<2 all come from 0<t<1 and -2<t<-1. I wrote this applet to go with an article I'm writing -- just to help get a feel for the parametric equation. Incidentally, Goldbach used a slick trick to solve, setting y=ax, substituting, and then setting t=1/(a-1).

 

dborkovitz

 
Resource Type
Activity
Tags
equation  equations  exploration  exponential 
Target Group (Age)
19+
Language
English (United States)
 
 
GeoGebra version
4.0
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