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Tetragonos Magicus: A Mathematical Journey Through Intriguing Artistry

Explore the fascinating world of mathematically inspired art with a focus on Tom Brylawski's ten-by-ten Graeco-Latin square that unveils the magical sum of 495. Discover historical breakthroughs like the disproval of Euler's conjecture and the revolutionary knot group relations presented by Brooks, Smith, Stone, and Tutte. Delve into the mystical realm of geometric progressions reflected in the iconic Affine Old Flag and Kempe's renowned four-color conjecture. Witness the evolution of mathematical visions through time, from ancient reflections groups to modernized graph interpretations. This journey invites you to experience artistry intertwined with mathematical brilliance.

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Tetragonos Magicus: A Mathematical Journey Through Intriguing Artistry

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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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