Re: riddle inside a riddle

Sam Evers (severs@SA.UA.EDU)
Fri, 17 Jan 1997 10:55:03 -0600

I don't remember the technical name (or if there even is one), but
I've heard this called the "hairy ball theorem". At least I think
this is it. The theorem goes something like: If you have a ball with
an infinite number of hairs covering the surface, it is impossible to
"comb" the hairs so that none are perpendicular to the surface. At
least one will always be perpendicular In it's more mathematical
form, this is a theorem on vectors. In this form, the perpendicular
hair is the house located at the north pole.

On a similar note, we've heard the puzzle about the man who is hunting
bear. He hikes 1 mile south, tracks a bear 1 mile east, loses the
bear and returns 1 mile north to his camp only to find it ravaged by a
second bear. What color were the bears? The puzzle appears the same,
and technically it is the same. But mathematically, this scenario
could take place somewhere besides the north pole. Where?

Happy puzzling,
Sam Evers
Multimedia math
University of Alabama

______________________________ Reply Separator _________________________________
Subject: riddle inside a riddle
Author: Steve Kraisler <stevek@FORUM.SWARTHMORE.EDU> at smtp-link
Date: 1/13/97 4:23 PM

WHAT THEOREM OF CALCULUS IS ILLUSTRATED BY THIS PUZZLE?

"A man builds a rectangular house that has southern exposure on all four
sides. Where does he live??
Steve Kraisler Intrnet: stevek@forum.swarthmore.edu
Mathematics Dept. stevek@icdc.com
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