Adventures in Symmetry
Symmetry
1. Correspondence in size, shape and relative position of parts that
are on opposite sides of a dividing line or median plane or that are
distributed about a center or axis; in a body, a design, a grouping
etc., an arrangement or external form marked by bylateral comformity,
geometric regularity or the like.
2. a. mutual relationship of parts as in size, arrangement, measurements
etc.; proportion b. due or balanced proportions; beauty of form arising
from such harmony c. a beautifully proportioned body. d. conformity;
consistency; congruity.
Tyger! Tyger! burning bright
In the forests of the night,
What immortal hand or eye
Could frame thy fearful symmetry?
As you can see from the definition above, and from
the words of Blake's poem The Tyger, there is more to symmetry than just
the mathematical.
As I set out to write the manual on how to use SymmeToy, I quickly
realized that this could not cover many, many aspects of my interest in
the subject of symmetry. Where would my exploration of various
symmetrical Disney attractions fit into such a book? How could I include
the strange story of how a chance footnote in a paperback novel led me
to dig for treasure in a heap of rubble on the outskirts of London? Or
how, after 20 years of trying, I brought a dead man back to life? Or,
how I finally discovered the secret of time travel?
After many a false start, I finally decided to make two little books.
One would explain how to use the program, and a second would tell of my
other explorations in symmetry. These web pages are from the second of
these books, translated for consumption on the Internet.
The stories in this section tell how I became interested in mathematical
symmetry. This first section contains a series of autobiographical tales
about places I have found to be wonderfully symmetrical, places like a
cathedral in Quebec, a museum in France and a rug show right here in my
own small Pennsylvania town. At first reading you may not understand why
I think some of these stories are symmetrical, but I hope that on
further thought you will find in them the same symmetry that I do.
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