From: chenrich@monmouth.com (Christopher J. Henrich)
Newsgroups: sci.math
Subject: Re: Help! Magic Squares
Date: Sat, 23 Mar 1996 12:19:31 -0500
In article , rasx@netcom.com (Bryan Wilhite) wrote:
> Recently, it has been brought to my attention the subject of "magic
> squares." They appear to be matrix-like entities that take a series of
> numbers arranged (matrix-like) such that they add up to the same sum
> (even when the numbers are added along a diagonal).
>
> If there are any brilliant blokes out there that know what these things
> are --and if they are treated by some area of number theory unknown to me--
> please let me know. Thanks very much in advance.
>
> --
This question recurs from time to time in sci.math. Does it qualify as
an FAQ? In any case, here is a response.
A bibliography on Magic Squares.
The following is terribly incomplete. The subject has attracted amateur
and professional attention for centuries, and the literature is enormous.
These books are recent and relatively available. (In fact, they have all
been published or reprinted by Dover Publications, and are available as
sturdy, reasonably priced trade paperbacks. I have no connection with
Dover except that of a lifetime fan.)
W. S. Andrews, Magic Squares and Cubes.
William H. Benson and Oswald Jacoby, Magic Cubes: New Recre4ations.
William H. Benson and Oswald Jacoby, New Recreations with Magic Squares.
These two books devote substantial space to this topic among others:
W. W. Rouse Ball & H. S. M. Coxeter, Mathematical Recreations and Essays
M. Kraitchik, Mathematical Recreations.
The magic squares of order 4 are completely known: there are 880 of them.
See:
Kathleen Ollerenshaw and Herman Bondi, Magic squares of order 4, in the
_Philosophical Transactions of the Royal Society of London_, Series A,
vol. 306 (1982) 443-532.
Last and least,
Christopher J. Henrich, Magic Squares and Linear Algebra, in the _American
Mathematical Monthly, vol. 98, No. 6, June-July 1991, 481-488.
Regards,
C. J. Henrich
--
Christopher J. Henrich
chenrich@monmouth.com