Aesthetic Appeal of Magic Squares

Russell Jay Hendel
Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture (2013)
Pages 573–574 Short Papers


Magic squares are rectangular arrays of numbers whose row, column and diagonal sums are all equal. Magic squares are frequently constructed from underlying square designs with certain symmetries. However, these symmetries are hidden to the viewer who only sees the numbers. Consequently, it superficially appears that the driving appeal of magic squares is their numerical properties. In a recent paper, Fang, Ming and Jianmin provided statistical evidence that magic squares have superior aesthetic appeal over random squares. In this paper, we retest this conjecture on aesthetic appeal using a different more appropriate statistical test. We test the hypotheses that i) the numbers in a magic square or ii) the symmetries in the underlying square design enhance aesthetic appeal. Our conclusion is that while magic and symmetry-based squares superficially appear to have superior aesthetic appeal, this superiority is not statistically significant.