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?"

Wayne

At 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