## 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.
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[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 The Magic Array Problem, (unpublished lecture notes).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.