{"id":"magic-square","domain":"recreational","type":"Concept","title":"Magic Square","slug":"magic-square","url":"/mathematics/recreational/magic-square/","summary":"A grid of numbers where every row, column, and diagonal sums to the same total. Known across Chinese, Indian, Islamic, European cultures for 2000+ years.","magic_constant_formula":"M = n(n^2+1)/2 for n x n square using 1 to n^2","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Andrews, W.S. (1917, Dover reprint 1960). Magic Squares and Cubes. Dover Publications."},{"tier":2,"citation":"Pickover, C.A. (2002). The Zen of Magic Squares, Circles, and Stars. Princeton University Press."},{"tier":2,"citation":"Cammann, S. (1960). The evolution of magic squares in China. Journal of the American Oriental Society, 80(2), 116-124."},{"tier":3,"citation":"Kanigel, R. (1991). The Man Who Knew Infinity. Scribner."}],"relationships":[{"type":"related_to","target":"ramanujan","label":"Srinivasa Ramanujan — date-encoding squares"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"1.6"}