Symmetry and the Shape of Space

Pattern and symmetry are truly fundamental human concerns, of as ancient interest as rhythm and language, and appear in virtually every human culture. Vivid, sophisticated examples date to to paleolithic times. Below is a detail from a five-thousand year-old Cycladic "frying pan", a detail from a ceremonial digging board from Ica Valley, Peru, and a finely crafted container from Zaire.

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Symmetry surrounds us, both in the natural world and in the world of human artifact. As you walk around in the coming week or two, be aware of the patterns surrounding you-- the arrangement of needles on a pine tree, the sculpture in a hubcap, the vortices in the Mississipi River, the slats in a set of blinds...

Mathematicians are relative newcomers to the symmetry game, and certainly have their own set of pre-occupations, but offer an extremely useful, beautiful, and even surprising view.


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  Chaim Goodman-Strauss
  Dept. Mathematics
  Univ. Arkansas
  Fayetteville, AR 72701