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Discover the extraordinary tetragonal magic square by Brylawski, UNC-CH, a Graeco-Latin masterpiece of dynamic numbers and rows. Explore mathematical art from Bose, Parker, Shrikehande, and more, reshaping Euler's conjectures and unveiling the complexities of squares and knots. Engage with the captivating history of mathematical art, including Kempe's pioneering work on the four-color conjecture and its modern proof by Appel, Haken, and computers. Dive into the world of reflection groups and crystallographic wonders, including intricate patterns and group theory revelations. Join the journey through mathematically inspired art, where creativity meets precision in a realm of infinite possibilities.
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Mathematically Inspired Art Tom Brylawski, UNC-CH
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)
Squaresville First square dissected into unequal squares by Sprague; Brooks, Smith, Stone, and Tutte (1940)
Presentation for a Sailor Generators and relations for the knot group of a (sculptural) bowline knot.
Affine Old Flag American flag draped vertically with a vertical compression
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)
Visions from the Tomb: A Table of Reflection Groups The seven planar crystallographic groups whose quotient by the subgroup generated by reflections is compact
