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From: eklhad@ihnet.UUCP (K. A. Dahlke)
Newsgroups: net.math
Subject: Re: Use the right newsgroup, please
Message-ID: <325@ihnet.UUCP>
Date: Mon, 18-Nov-85 15:19:19 EST
Article-I.D.: ihnet.325
Posted: Mon Nov 18 15:19:19 1985
Date-Received: Tue, 19-Nov-85 04:27:42 EST
References: <268@epicen.UUCP>
Distribution: net
Organization: AT&T Bell Laboratories
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> 2) Traveling polar bears. This is what net.puzzle is for. I know that a lot
>    of net.math people like puzzles, but they read net.puzzle as well.
> Let's have more math in net.math. 
> Joe Buck

Certainly the first polar bear problems were not very original,
and they required more creativity than mathematics.
However, I think the most recent sequel, "traveling" polar bears,
belongs in net.math.  (Should have picked a different title).
Unless I am missing an obvious solution, it seems to require
a fair amount of math, at least to prove the answer.
It may not be graduate math, but it is interesting (to me) nonetheless.

The problem, for those of you who self-righteously skipped it,
was essentially this:
Construct a topography, such that a bicycle equipped with square
wheels has a smooth ride when traveling over this terrain.
I started thinking about the problem, and decided it was ambiguous.
Thus, the reason for this article.
Can the originator of this problem define "smooth" ride for me.
One possibility is "level" ride.  That is, the rider
doesn't move up and down.  Another possibility is an "inertial" ride.
That is, the speed is constant, for a given
peddling rate.
Perhaps both conditions must be satisfied (seems unlikely).
Perhaps the "energy" expended by the rider should be constant, for a given
peddling rate (no need to shif gears).
Please clarify.  Thanks.

Does this problem have a more general solution,
say for bicycles with N-sided wheels?
Are there wheels which never permit a smooth ride?
-- 
	Nothing's worse than a dishwasher full of spotty dishes.
			Karl Dahlke    ihnp4!ihnet!eklhad