Information About Topology

Date: 11/12/96 at 00:42:40
From: Chitur V Prakash
Subject: topology

Hi,

I am a tenth grade student currently enrolled in an honors geometry 
class.  One of our assignments is to do a project on a certain aspect 
of geometry and I have chosen topology. If you have any information 
pertaining to the subject, or can head me in the right direction as to 
where to research, please contact me. I am especially interested in 
information about when topology was invented, who invented it, where 
it was invented, modern day uses, and example exercises.

Thanks again.

Date: 11/13/96 at 11:59:37
From: Doctor Jodi
Subject: Re: topology

Hi there! Thanks for your question - I love topology. Topology is 
sometimes called "rubber sheet geometry" because it deals with 
stretching and compressing objects.

To find out more about the history of topology, look at:

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Topology_in_mathematics.html   

Where is topology used today?

COSMOLOGY:

Topology is related to a field called cosmology, which asks about the 
shape of the universe. You can find out more about this by looking at:

  http://www.geom.uiuc.edu/docs/forum/sos/   

This site talks about _Shape of Space_ by Jeff Weeks, a book, movie, 
and curriculum. The book is really accessible, so if you find out that 
you're interested in DOING a little topology, you should check it out.

TURNING A SPHERE INSIDE OUT:

You can find out more about another Geometry Center movie, _Outside 
In_, by reading the script and looking at accompanying pictures at:

  http://www.geom.uiuc.edu/docs/outreach/oi/script.html   

_Outside In_ talks about how to turn a sphere inside out using 
topology. 

KNOTS AND DNA RESEARCH:

Did you know that your DNA has knots in it?  Mathematicians have been 
interested in studying knots since Lord Kelvin (about 150 years ago) 
suggested that atoms were different from each other because of 
"knotted vortices."  Even after scientists discarded that idea, 
mathematicians continued to be interested in knots. In the past 10 
years or so, the branch of topology known as knot theory has found new 
applications in DNA research. You can find out more about knot theory at: 

  http://www.c3.lanl.gov/mega-math/gloss/knots/knots.html    

(I highly recommend this site because you can get up to speed on 
questions that researchers are currently working on and even help find 
the answers to those questions.  I spent the summer of 1996 as an 
undergrad researcher in knot theory.  We got some cool results on open 
problems.  A dedicated high school student could do the same!)

CRYSTALLOGRAPHY:

Topology, tilings and tesselations also relate to crystallography, 
which is used by chemists. I don't know much about this, but what I've 
heard sounds really interesting.

Other place to look for topology:

You might also enjoy looking at the Geometry Center's Topological Zoo 
at:
 
  http://www.geom.uiuc.edu/zoo/   
 
which has a lot of pictures and animations of mathematical objects.

You'll also want to play with their Interactive Gallery of Geometry:
 
  http://www.geom.uiuc.edu/apps/gallery.html   

I hope this helps... If you have any other questions, let us know.

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