Knot Theory

Date: 10/24/96 at 23:15:18
From: Neil Sen-Gupta
Subject: Knot Theory

Dear Dr. Math,

I am in the tenth grade, and we are doing a research report on Knot
Theory. I have found many sites with knots and examples, but so far I
have not yet found a definition of the Theory which describes its
purpose or function. Would you happen to know what Knot Theory
actually describes and means, what it states about knots, and its
usefulness in real life? Finally, is Knot Theory really a Theory
about types of knots, or is it just a certain field of mathematics?
							
Sincerely,
			Neil

Date: 10/25/96 at 12:48:58
From: Doctor Ceeks
Subject: Re: Knot Theory

Hi,

You can think of a knot as a loop of string.

Sometimes, you can take a knot and fiddle with it (without cutting
it!) and turn it into a simple circular loop of string.
Sometimes you can't.

When can you do that?

If you try to find a definitive answer to that simple question,
you end up creating knot theory.

Knot theory is both a mathematical theory and a field of mathematics.
It is a theory because it is rich in interconnecting ideas.  It is
an active field of research because that simple question hasn't been
answered yet!

-Doctor Ceeks,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/