Mathematically Inspired Art

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Mathematically Inspired Art

• Tom Brylawski, UNC-CH

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?????????? 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)

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Squaresville

• First square dissected into unequal squares by
  Sprague Brooks, Smith, Stone, and Tutte (1940)

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Presentation for a Sailor

• Generators and relations for the knot group of a
  (sculptural) bowline knot.

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Affine Old Flag

• American flag draped vertically with a vertical
  compression

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Back to the Drawing Board

• Kempes proof published in 1879 (somewhat
  modernized to graphs instead of maps) to the
  four-color conjecture with Heawoods
  counterexample published 11 years later (!)
• Subsequently modified by Appel, Haken, and
  computer to a correct proof (1977)

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Visions from the Tomb A Table of Reflection
Groups

• The seven planar crystallographic groups whose
  quotient by the subgroup generated by reflections
  is compact

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p6m
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p31m
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p3m1
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pmm
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p4g
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cmm
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p4m