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Symmetry: Culture and Science
Volume 32, Number 2, pages 145-148 (2021)


Dave Everitt1, Fania Raczinski2

1 30 Woodland Avenue, Melton Mowbray, LE13 1DZ, United Kingdom
E-mail: dave.everitt@me.com
Web: https://daveeveritt.org/art.html
ORCID: 0000-0002-2929-6023

2 E-mail: me@fania.eu
Web: https://fania.eu
ORCID: 0000-0001-5400-1031

Abstract: When considering magic squares (number grids with a constant sum for each row, column and diagonal), rotations and reflections are considered trivial. Our investigation uses the magic line (connecting each integer in sequence) to reveal underlying homologies and to investigate whether magic squares that share magic line patterns might also be considered trivial. We have written software (also used to create artistic creative magic line visualisations and animations) to aid this process. The mathematics is simple but magic square variations are deceptively complex and overlapping. Simplification, using homologous patterns, is the subject of this paper.

Keywords: magic squares, combinatorics, number theory, group theory, permutation.
PACS 2010: 02.10.Ox, 02.10.De, 02.20.-a

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