Abstract

Previous abstract Back to issue content Next abstract
Symmetry: Culture and Science
Volume 32, Number 2, pages 145-148 (2021)
https://doi.org/10.26830/symmetry_2021_2_145

MAGIC SQUARE PATTERN HOMOLOGIES

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

References:
Danielsson, H. (2020) Selbstkomplementäre magische Quadrate. In: Magische Quadrate. [online] magic-squares.info [9 May 2021]. https://www.magic-squares.info/docs/magische-quadrate.pdf

Evertt, D., Raczinski, F. (2020) Creative Visualisation of Magic Squares. In: Proceedings of 30th Conference of Electronic Visualisation & the Arts, London (EVA2020). 16-19 November 2020, London, UK [online]. BCS: The Chartered Institute for IT. pp. 217-224. https://doi.org/10.14236/ewic/eva2020.39

O’Connor, J.J., Robertson, E.F. (2014) Bernard Frénicle de Bessy. [online] MacTutor [9 May 2021] Available from https://mathshistory.st-andrews.ac.uk/Biographies/Frenicle_de_Bessy

Heinz, H. (2010) Order 4, Transformations & Patterns. [online] magic-squares.net [9 May 2021] Available from http://www.magic-squares.net/transform.htm

Suzuki, M. (2019) The 880 Magic Square of 4 x 4, [online] Math Forum archive [9 May 2021] Available from https://web.archive.org/web/20060708024749/; http://mathforum.org/te/exchange/hosted/suzuki/MagicSquare.4x4.total.html