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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)
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.
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