Unfolding the mystery behind an affine magic square

• Main Authors: Aterrado, Katherine M., Mijares, Emma Ruth C.
• Format: text
• Language: English
• Published: Animo Repository 1995
• Subjects: Geometry, Affine; Magic squares; Numbers, Theory of; Mathematical recreations
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16315
• Institution: De La Salle University

This thesis aims to define what an affine magic square is and to determine the number of existing affine magic squares. An affine square is the square determined by the map W = 8V1(x) + 4Vz(x) + 2V3(x) + V4(x) + 1 where Vj, j = 1, ...,4 are affine functions. An affine magic square is nonsingular and has the same sum on its rows, columns and main diagonals.The number of affine magic squares which exist is the product of the following: the number of sets of nonsingular eligible linear functions, the number of sets of affine functions, and the number of ways in which these functions can be arranged. But a square has 8 symmetries. Thus, the product is divided by 8 to get the number of distinct affine magic squares.An example of an 8 X 8 affine magic square is given. But due to time constraints, a detailed account of higher order affine magic squares cannot be given.