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Symmetry: the responses
Posted:
Jul 20, 1995 9:05 AM


Hello again!
A few days ago I asked about symmetry references. This is a compilation of the responses I received. I have tried to thank each of the responders personally, and if I forgot anyone, I apologize. All responses were greatly appreciated! The following are excerpts of the messages I received. Any misrepresentation as a result of my "snipping" is unintentional. The items are divided up into Web sites, books, software, and miscellaneous ideas. Enjoy!
  Web sites:  I would refer you to the Web location http://www.geom.umn.edu and under downloadable software you will find two Macintosh programs which may be of interest: KaleidoTile and Kali. Both programs have been developed at the Geometry Center and focus on symmetry.
At http://www.geom.umn.edu/~strauss you will find an excellent collection of notes on symmetry assembled by Chaim GoodmanStrauss, a postdoc at the Geometry Center.
Arnie Cutler K12 Education Coordinator The Geometry Center   Books, booklets, etc.:  "Elementary School Mathematics; teaching developmentally" by John A. Van de Walle, NY & London: Longman (2d. edition, 1994) Chapter 17 has many excellent ideas and many blackline masters at the back, as well.
Richard Fouchaux  I recommend the following collections of activities by John C. Huber of Sam Houston State University. All are quite recent and, I believe, are currently produced "in house" at Sam Houston.
An Introduction to Reflections Using the MIRA The Geometry of Frieze Patterns The Geometry of Tesselations
Ron Ward/Western Washington U/Bellingham, WA 98225  It's been more years than I care to remember since I last taught math, but, when I did, I taught several sections of basiclevel geometry to high school students. (In many places today, this course would be called "informal geometry.") I felt that the presentation of symmetry in the existing textbooks was abysmal. Then I discovered the unit on symmetry in the Harold Jacobs book, Mathematics: A Human Endeavor. The suggested presentation is very laborintensive for the teacher, but I felt that the payoff was stunning. The presentation and suggested activities generated more excitement in students than I saw with any other materials. Most importantly, I felt that most students came away from the unit with a fairly sound understanding of symmetry. An added benefit: I learned a lot, too. ... This particular unit does move on into areas that you might not be interested in pursuing: regular polygons, tessellations, regular and semiregular polyhedrons, pyramids, prisms, and so on. ...
The information about the book is as follows:
Mathematics: A Human Endeavor Harold R. Jacobs W.H. Freeman and Company San Francisco copyright 1970, 1982
This is the second edition of the book. I'm not sure, but I think there may also be a more recent edition. Whichever edition you might obtain, be sure to get the accompanying teacher's guide.
Marie Power (freelance writer/editor of elhi math materials) South Bosotn, MA  The UCSMP Geometry text treats [transformation] extensively  all of Chpt. 6 I believe. There are lots of ideas there. A popular one  with students  is miniature golf and billiards. These would lead to some good models. Hope this is helpful!
Katherine G. Harris  Shelter Publications publish a book named, "Symmetry". I saw it briefly at a book convention. I think it show the symmetry of structures, new and very old. It was being distributed through: Ten Speed Press P.O. Box 7123 Berkeley, CA 94707
Johnny Hamilton Construction Trades Press  ... I have one other reference to suggest:
The Ambidextrous Universe: Mirror Asymmetry and TimeReversed Worlds Martin Gardner Charles Scribner's Sons New York copyright 1979, 1969, 1964
As you can guess, this is not a source of classroom activities, per se. Rather, it is a fascinating (I think!) discussion of the symmetry of the natural world, the manmade symmetries that mimic it, and the long search for  and ultimate discovery of  natural phenomena that are asymmetric ("the downfall of parity"). I found it interesting reading for myself, and I was able to glean ideas for classroom use from it. If you will be teaching college students again, most of them should be able to handle the text if you were to suggest it on a reading list. (You have to have some level of comfort with reading science in order to get all the way through it, but it is most definitely not highly technical reading.) A capable, motivated high school student should also be able to read it and benefit from it.
Marie Power  ...note that several of the units in the Investigations in Number, Data, and Space# curriculum deal extensively with this subject. The unit, "Flips, Turns, and Areas" includes a macintosh software program that looks like the software game, Tetris, in which the user manipulates tetrominoes using slides, flips and turns, in order to fill up a bin with as few spaces as possible.
Merle Silverman Product Research and Development Dale Seymour Publications   Software and associated materials:  There is a very good computer program created by MECC called TESSELMANIA. It demonstrates rotation, reflection etc.
Eileen Abrahamson Edw. Neill Elemetary, Burnsville, MN 55337  Have you ever used LOGO? I've used it for lessons on symmetry, rotations, etc. Kids love it. ...Earlier I recommended LOGO as a tool for students to explore all the topics you're interested in. Specifically, I'd recommend an excellent little book entitled "Tesselations with LOGO". It's available from either Creative Publications or _________(darn it, I can't remember. You know, the other mail order house. It's slipped my mind.) Somebody'll know.
Great little book.
Dan Hart SFHS LAUSD
This was also suggested by Merle Siverman (see previous item)   Miscellaneous ideas:  Symmetry was the basis of Soviet (and probably still is) Army tactics and doctrine. I am a retired cavalry officer now pursuing a master's in secondary education (mathematics). When I revisited my old briefing slides and instructional aids on Soviet armored formations  espeically from the platoon to the brigade in the attack, the symmetry was amazing.
And its their doctrine. Everyone and every leader must be in the precise (and I mean to within 5 to 10 meters) in their formations. They believe in mass.
There the symmetry helps there mass to achieve combat power, but works to our advantage as it helps us identify where the "leaders" were to destroy their command and control.
... symmetery works. . . even in combat.
Stephen P. Balint Graduate Student  UNLV  If I were to think about symmetry and color relationships, I would look at the painters Cezanne and Josef Albers. Mondrian's work deal more in assymetrical color and line relationships.
Johnny Hamilton  One place to find the various symmetries is on good old fashioned wallpaper. Why not get some and try to "hang it"?
Doug Hale 
Thanks everyone!
Murphy
 Murphy Waggoner Department of Mathematics Simpson College 701 North C Street Indianola, IA 50125 waggoner@storm.simpson.edu 



