```Date: Jun 21, 2013 8:01 PM
Author: Wayne Bishop
Subject: Re: new tutor here

How do either of you respond to the smart-ass student who says:"My calculator says e^pi ~ 23.14 and pi^e ~ 22.46.  Why are we wasting time on this?"WayneAt 07:43 PM 6/18/2013, Joe Niederberger wrote:>R Hansen states:> >Back to the use of visualizations in school. Two scenarios...>1. I show the students your visual proof that e^pi > pi^e and I ask >them "Do you see that e^pi > pi^e?">2. I show the students your visual proof that e^pi > pi^e and I ask >them "How does this prove that e^pi > pi^e?">>I wouldn't expect either to make much sense, though with some >rewording I would say [2] could be something approaching an >"exercise" (which is all the original problem is.) the original >problem is a nice classic exercise because it allows many different >proofs, none of them long. I decided to solve it as I did quite >intentionally, (in my head, visually), just to add a twist.>>I must say again, I wouldn't use either of your {1] or [2] in >school; the original is better, simply: Which is larger..etc. I see >little value in trying to mold people in one direction.>>Here's the pic:>Simply the log (ln) curve, with points where it intersects (e,1) and >(pi,log(pi)) noted.>>As simple as it seems, I had to sort through a few contenders to >pick that one as having just the right relations expressed and >"close to the surface" -- all assuming a little background of course.>>If there's simpler picture that "says it all" I'd like to know.>>Cheers,>Joe N
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