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Topic: Symmetry: the responses
Replies: 1   Last Post: Jul 21, 1995 3:37 PM

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Murphy Waggoner

Posts: 52
Registered: 12/6/04
Symmetry: the responses
Posted: Jul 20, 1995 9:05 AM
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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
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 you will find an
excellent collection of notes on symmetry assembled by Chaim
Goodman-Strauss, a post-doc at the Geometry Center.

Arnie Cutler
K-12 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
black-line 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 basic-level 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 labor-intensive 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 Time-Reversed 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 man-made 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

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 Waggoner
Department of Mathematics
Simpson College
701 North C Street
Indianola, IA 50125

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