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What is Knot Theory?


Date: 03/10/98 at 23:46:23
From: keatha
Subject: the knot theory

Dear Dr. Math,

In order for me to complete my project on knot theory, I need a 
question, hypothesis, and a purpose. I have this information, I just 
want you to proofread it to see if I need to add anything or delete 
anything.

Question: What is Knot Theory?
Purpose: To prove that knot theory is related to topology.
Hypothesis: If topology deals with the bending of objects, then it 
(knot theory) is related to topology.

Thanks a million,
Keatha


Date: 03/11/98 at 10:32:24
From: Doctor Sonya
Subject: Re: the knot theory

Dear Keatha,

I just wrote a big paper on knot theory. What a great topic to choose. 
Your question is good, and your hypothesis is correct -- that topology 
deals with the bending of objects, and that topology is related to 
knot theory. However, if you really want to answer the question, "What 
is knot theory?" I don't think, "Knot theory is related to topology." 
is enough of an answer. When you get to the real details of it, knot 
theory is also closely related to modern algebra (although you'd never 
know it from all the pretty pictures of knots!).

The most exciting thing about knot theory that deals with the bending 
and twisting of knots is something called the "Jones Polynomial," 
discovered by a mathematician named Jones and written about by Louis 
Kauffman. If you still have to do more research, this might be 
interesting for you to include. Also, take a look at

"The Knot Theory Home Page"
   http://tqd.advanced.org/12295/main.html   

Good luck with your project.  

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