Symmetry
If you look at objects in nature, you'll find no shortage of examples of symmetry -dragonflies, snowflakes, even your own hands. We'll talk with a mathematician about symmetry - after this on Earth and Sky.
Date
(Tape 0:02:50-0:02:57) Symmetry occurs in nature -- that's the reason it's important. And when it does occur, it affects how things behave.
DB: This is Earth and Sky, and you're listening to Dr. Michael Artin of the Massachusetts Institute of Technology talking about symmetry. A thing is symmetrical if there's some way that you can transform it so that it looks the same as it did when you started.
(Tape 0:00:14-0:01:02) So for symmetry of things, plane figures, there're three kinds, three basic kinds - and then they can be combined. And the three kinds are first of all left-right symmetry, so you might have a stick figure and it's symmetric with respect to left-right. Or the second kind would be rotational symmetry, like a square has 90-degree rotational symmetry. And the third kind is the symmetry that a wall-paper pattern has - it's called translational symmetry. And that means that if you take the wallpaper and shift it over a certain distance in some direction, that you'll get the same pattern back. (Tape 0:02:57-0:03:14) So for instance crystals have what's called a translational symmetry, although it's in three dimensions. The atoms in a crystal are distributed uniformly and you can move the crystal to one side or another and the pattern will repeat. (0:03:26-0:03:29) And that affects how the crystal behaves, chemically.
DB: Thanks to Dr. Michael Artin for speaking with us. And with thanks to the National Science Foundation, I'm Deborah Byrd, for Joel Block, for Earth and Sky.
Author: Beverly Wachtel
Thanks to the following individual for aiding in the preparation of this script:
Dr. Michael Artin
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
Artin@math.mit.edu
If you enjoyed this program, you may be interested in the following websites:
Math Forum - Types of Symmetry:
http://forum.swarthmore.edu/sum95/suzanne/symsusan.html
Symmetry Web:
http://www.math.okstate.edu/mathdept/symmetry/
Mathematical Sciences Research Institute:
http://www.msri.org