Mathematically Inspired Art

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)

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

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

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

10. 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)

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

14. p6m

15. p31m

16. p3m1

17. pmm

18. p4g

19. cmm

20. p4m