Links and References for Magic Squares

Links

Dürer's Melencolia is the subject of a vast amount of commentary. The Wikipedia page gives some pointers to some of it.

Alexander Bogomolny has a Web site with interesting and interactive treatments of many topics, including magic squares.

Christian Boyer's web site "Multimagie.com" is a rich source of information on multimagic squares. (French, English, and German versions.)

Harvey Heinz's web site Magic Squares, Magic Stars & Other Patterns describes many variations on the magic square, with many links to other sites. He also has a Web site devoted to magic cubes.

"Grog" Grogono maintains a Grogono Magic Squares page with (more informally stated) a similar technique to mine.

Susan Alejandre maintains a site with, among other things, a magic square due to Ben Franklin.

Paul C. Pasles has a web site devoted to Ben Franklin's magic squares.

Mitsutoshi Nakamura maintains a site devoted to "Magic cubes and tesseracts."

Books and Papers

Magic Squares and "Mathematical Recreations"

•Adler, Allan, "Magic cubes and the 3-adic zeta function", Math. Intelligencer 14(1992), no. 3, 14-23.

• Ahmed, Maya Mohsin, "How Many Squares Are There, Mr. Franklin? Constructing and Enumerating Franklin Squares", american Mathematical Monthly, 111 (2004) 394-410

• Andrews, W. S. Magic Squares and Cubes, 1917, reprinted 1960 Dover Publications, ISBN 0-486-20658-0

• Benson, William H.; Jacoby, Oswald New Recreations with Magic Squares, Dover Publications, New York 1976, ISBN 0-486-23236-0

• Benson, William H.; Jacoby, Oswald Magic Cubes New Recreations, Dover Publications, New York 1981, ISBN 0-486-24140-8

• Derksen, Harm; Eggermont, Christian; van den Essen, Arno: "Multimagic Squares", American Mathematical Monthly, 114 (2007) 703-713

• Henrich, Christopher J., "Magic Squares and Linear Algebra", American Mathematical Monthly, 98 (1991) 481-488

• Kraitchik, Maurice, Mathematical Recreations, second revised edition, 1942, reprinted 1953 Dover Publications, New York, ISBN 0-486-45358-8

• Ollerenshaw, Dame Kathleen; Bondi, Sir Herman: "Magic Squares of Order 4," Phil. Trans. Royal Soc. London, 306 (1982)443-532

• Pasles, Paul C.: The Lost Squares of Dr. Franklin, American Mathematical Monthly, 108 (2001) 489-511. For updated information, see the author's web site.

•Zhu, F. C., "On Nasik Magic Cubes and Hypercubes," in Combinatorics and Graph Theory, Proceedings of the Spring School and International Conference on Caombinatorics, Hefei, China, 6-27 April 1992, ed. H. P. Yap, T. H. Ku, E. K. Lloyd, and Z. M. Wang; pp. 91-94.

Linear algebra

• Axler, Sheldon Linear Algebra Done Right, Second Edition, Springer, ISBN 0-387-98258-2

• Curtis, Charles W. Linear Algebra: an Introductory Approach, Springer, ISBN 0-387-90992-3

• Halmos, Paul R., Finite-Dimensional Vector Spaces, New edition reprinted by Springer, ISBN 0-387-90093-4

This is a classic text and reference.

• Hausner, Melvin A Vector Space Approach to Geometry, Dover, ISBN 0-486-40452-8

• Kaplansky, Irving Linear Algebra and Geometry: a Second Course, Dover, ISBN 0-486-43233-5

Counting Problems

• Ollerenshaw, Dame Kathleen; Brée, David Most-Perfect Pandiagonal Magic Squares. Their consttruction and enumeration, The Institute of Mathematics and its Applications, 1998. (May be ordered from the IMA.)

Last modified on $Date: 2015-05-02 12:51:16 -0400 (Sat, 02 May 2015) $

Christopher J. Henrich