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On the symmetries of a Grecian urn

Published online by Cambridge University Press:  01 August 2016

Diogenes O’Rell
Diogenes O’Rell*
Affiliation:
School of Mathematics, University of Leeds, LS2 9JT
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Extract

      While musing on the graceful sylvan scene
      Depicted on a classic Grecian urn,
      John Keats declared that “truth” and “beauty” mean
      The same, and here this statement’s worth we learn.

      “Thou still unravish’d bride of quietness!
      Thou foster-child of Silence and slow Time”,
      Wrote Keats [1], the um’s calm beauty to express,
      While he, by permutations of the rhyme,
      Did generate its group of symmetries,
      Which is dihedral and of order six.
      The um and its inversion therefore match
      And all its patterns replicate in threes:
      So triplet dancers demonstrate their tricks
      While silent pipers play a triple catch.

Type
Research Article
Information
The Mathematical Gazette , Volume 76 , Issue 476 , July 1992 , pp. 269
Copyright
Copyright © The Mathematical Association 1992

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References

1. Keats, J., On a Grecian urn.Google Scholar
2. Shakespeare, W., Sonnet 65.Google Scholar
3 Van der Waerden, B.L., Modern algebra (revised English edition) pp 149–150, Frederick Ungar (1953).Google Scholar
4. Gorenstein, D., Finite simple groups. Plenum press (1982).Google Scholar