Volume 39, Number 20 · December 3, 1992
A–Symmetry
By Martin Gardner
Fearful Symmetry: Is God a Geometer?
by Ian Stewart, by Martin Golubitsky
Blackwell, 287 pp., $24.95
Symmetry in Chaos: A Search for Pattern in Mathematics, Art and Nature
by Michael Field, by Martin Golubitsky
Oxford University Press, 218 pp., $35.00
M.C. Escher: Visions of Symmetry
by Doris Schattschneider
W.H. Freeman, 354 pp., $24.95 (paper)
Wordplay:Ambigrams and Reflections on the Art of Ambigrams
by John Langdon
Harcourt Brace Jovanovich, 172 pp., $18.95
When Blake wrote of the Tyger's 'fearful symmetry' he was using the noun as a synonym for beauty. Today the word usually means any kind of regular pattern. Geometers sharpen the definition by making symmetry the property of a figure that stays the same after a given operation is performed. A snow crystal, the Star of David, and patterns in a kaleidoscope, for examples, have hexagonal or six-fold symmetry because they look the same after a rotation through any multiple of sixty degrees. You and the tiger have bilateral or mirror reflection symmetry because you both seem unchanged after a mirror has exchanged left and right sides. A wallpaper pattern has translation symmetry, meaning it is unaltered when shifted in any direction. If every other unit of a periodic pattern is mirror reversed, such as $$$…, the symmetry is called a glide reflection.
Review, 3071 words
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