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 FlagAmerican 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

p6m

p31m

p3m1

pmm

p4g

cmm

p4m