Binary Color-Coded Magic Squares: A Study of Uniqueness Under Rotation/Reflection, PCA, and LDA Analysis

Autor:	Fahimi, Peyman
Rok vydání:	2023
Předmět:	Mathematics - General Mathematics
Zdroj:	Discrete Mathematics, Volume 347, Issue 1, January 2024, 113708
Druh dokumentu:	Working Paper
DOI:	10.1016/j.disc.2023.113708
Popis:	In this paper, we study the concept of "binary color-coded magic squares" by assigning two distinct colors to the even and odd numbers within a magic square. We investigate the uniqueness of patterns within these squares using three different analytical methods, including rotation/reflection, PCA, and LDA. Our investigation covers all 880 magic squares of order 4, all 48,544 associative magic squares of order 5, and all 368,640 Franklin magic squares of order 8. Our investigation reveals striking patterns that were previously unknown in traditional magic squares, shedding light on the potential for binary color-coded magic squares to contribute to the field of mathematics. Comment: 10 pages, 3 figures, 2 tables
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2307.09996 Zobrazit plný text záznamu View this record from Arxiv