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/
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