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Mathematically Inspired Art

Explore the brilliance of Tom Brylawski's ten-by-ten Graeco-Latin square, positively magical with all digits from 0 to 9 and sums beautifully to 495. Dive into historic milestones like Bose, Parker, Shrikehande disproving Euler's 1783 conjecture, Squaresville's first dissection by Sprague, and Sailor Knot Generators. Learn about Kempe's 1879 proof of the four-color conjecture, later corrected by Appel, Haken & computer in 1977, alongside reflections on the fascinating crystallographic groups. Discover the art and math intersecting in Brylawski's work and the intriguing explorations by renowned mathematicians over the years.

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Mathematically Inspired Art

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  1. Mathematically Inspired Art Tom Brylawski, UNC-CH

  2.  Magicus A ten-by-ten Graeco-Latin square using the digits from 0 to 9 so that every number from 0 to 99 appears, and every digit from 0 to 9 appears in every row and column, each giving a magic square sum of 495. Found by Bose (UNC-CH), Parker, Shrikehande (1960) disproving a conjecture of Euler (1783)

  3. Squaresville First square dissected into unequal squares by Sprague; Brooks, Smith, Stone, and Tutte (1940)

  4. Presentation for a Sailor Generators and relations for the knot group of a (sculptural) bowline knot.

  5. Affine Old Flag American flag draped vertically with a vertical compression

  6. Back to the Drawing Board Kempe’s “proof” published in 1879 (somewhat modernized to graphs instead of maps) to the four-color conjecture with Heawood’s counterexample published 11 years later (!) Subsequently modified by Appel, Haken, and computer to a correct proof (1977)

  7. Visions from the Tomb: A Table of Reflection Groups The seven planar crystallographic groups whose quotient by the subgroup generated by reflections is compact

  8. p6m

  9. p31m

  10. p3m1

  11. pmm

  12. p4g

  13. cmm

  14. p4m

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