Visual Magic Squares and Group Orbits I

Acknowledgements

We thank Mark Pais (7^th Grade, Ladue Middle School) for stimulating our recent interest in magic squares by asking his father (John) to help him extend a partial 4 ´ 4 numerical square to a magic square. The desire to help Mark understand magic squares, motivated us to find a better way to think about them ourselves.

Regarding the format of this article, we are grateful to the Journal of Online Mathematics and Its Applications for developing the general layout and navigation that we have used here.

References

[1] E. R. Berlekamp, J. H. Conway, and R. K. Guy (1982). Winning Ways, Volume 2: Games in Particular. London: Academic Press, Inc.

[2] L. Euler (1782). Recherches sur une nouvelle espèce de quarrés magiques, reprinted in Leonhardi Euleri Opera Omnia Series I volume VII, Teubner, Leipzig and Berlin 1923, pages 291-392.

[3] J. E. Humphreys (1996). A Course in Group Theory. New York: Oxford University Press.

[4] J. Pais (2001). Intuiting Mathematical Objects Using Diagrams and Kinetigrams. Journal of Online Mathematics and Its Applications 1 (2).

[5] J. Pais and R. Singer (in preparation). Visual Magic Squares and Group Orbits II.

[6] R. Singer (1974). The Magic Array Problem, (unpublished lecture notes).

[7] A. Slomson (1991). An Introduction to Combinatorics. London: Chapman & Hall.