Introducing a new reference book on magic squares, cubes, tesseracts, magic stars, etc.
Download the free Lexicon_sample.pdf (549 Kb). This is a faithful reproduction of about the first onequarter of the book.
Magic Square Lexicon: Illustrated

Summations The magic sum for an nDimensional Magic Hypercube of Order m is given by: S = m(1 + m^{n})/2 In a magic object, there are many lines that produce the magic sum. The table below, shows the minimum requirement of the number of lines for various types of magic hypercubes and is derived from the following equation: N = 2^{(r1)}n!m^{(n1)}/[r!(nr)!]
When r = 1, the number of orthogonals is given by N. As well, shown is the smallest order for the various classifications of pandiagonal, pantriagonal, etc. which is known. for each dimension. Some of the tesseracts are not known yet and some of these varieties have not been constructed yet. This table provides the minimum requirements for each category. Usually, there are some extra lines which may sum the magic sum, but not a complete set so as to change the category. It is possible that
when the tesseract is explored more fully, some additional classifications
will be found.


(email quoted and used by permission HH note: My address is now
changed)
Subject: Your book, Magic Square Lexicon:
Date: Fri, 22 Dec 2000 16:36:33 0800 (PST)
From: Charles Ashbacher <cashbacher@yahoo.com>
To: hdheinz@istar.ca, magiccubes@home.com
Thank you for sending me a copy of your wonderful book.
The following review will appear in the book reviews column of 30(4) of JRM.
(It appeared in JRM 31(1), 20022003, pp5960)
Review of:
Magic Square Lexicon: Illustrated, by H. D. Heinz and J. R. Hendricks
Published by Harvey D. Heinz, Surrey, BC, 2000.
174 pages, $25.00(paper). ISBN 0968798500.
Contact information: Harvey Heinz, 225688 152 Street, Surrey, BC V3S 3K2
email: harveyheinz@shaw.ca
Book Review
While magic squares have a long history, until I read this book, I had no idea how much
has been done in the last few decades. The basic principles that make up a magic square
can be used to create an enormous number of similar objects. There are magic cubes,
tesseracts, stars, circles, triangular regions, hexagons and just about every other shape
in existence. Further
complicating the mix are additional features such as using only prime numbers or numbers
whose squares also make the structure magic.
The purpose of this book is to introduce and explain these results. Designed in the format
of a dictionary, the topics are in alphabetical order for easy reference. Profusely
illustrated, nearly every topic is accompanied by an illustration, all of which are
welldone and make the topic completely unambiguous.
There is no doubt that magic squares will still be a popular field of mathematics one
hundred years from now. To me, it is also clear that at that time the publication of this
book will be considered a major event in the history of magic squarelike constructs.
This is one of the most impressive books I have ever read.
Reviewed by
Charles Ashbacher
Editor, Journal of Recreational Mathematics
Magic Square Lexicon: Illustrated is all about magic squares, magic cubes, magic tesseracts, magic hypercubes, magic stars, magic circles, etc. It gives you definitions, limits, examples, illustrations, tables, terminology and everything that you want to know about magic objects.
It is written by two men who have spent a lifetime studying the subject
and who have pooled
their knowledge and experience in order to produce this book.
The contents of this web site show a fair representation of Harvey Heinz’s work and interests.
The work of John Hendricks, may be seen at his
page on this site and also at http://www.magicsquare.de/.
In addition, John has published over 40 articles and papers on these subjects as well as a
half dozen books.
Learn about the geometry of ndimensional space through the medium of magic squares and cubes. The new concept of ‘perfect’ is shown applied consistently to magic squares, cubes, tesseracts, etc. Many tables provide comparisons between orders or dimensions.
This is a reference book. There is no other book on the market like it. There are many references to the latest uptodate research in this field. Did you even know that such mathematical items as inlaid magic cubes existed, or inlaid magic tesseracts?.
July 2005: The second print run (now selling) has all known errors corrected.
Need more information?
Download the free
Lexicon_sample.pdf (549 Kb). This is
a faithful reproduction of about the first onequarter of the book.
Copies of Magic Square Lexicon: Illustrated are available postage paid (in North America) by sending either a postal Money Order or a bank draft for $32.00 Canadian, or $25.00 U.S. funds per copy to:
H. D. Heinz, #22  5688 152 Street, Surrey, B.C.,V3S 3K2,Canada.
For additional information email harveyheinz@shaw.ca
Order a copy of this book today, for yourself or a friend !
Copies mailed outside North America are $30.00 U. S,
including airmail postage.
Possibly the simplest and least expensive method is to send $45.00 Canadian funds
via Western Union
(see your local money store). You must notify me of this because Western Union does not contact the recipient).
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This page last updated
December 18, 2005
Harvey Heinz harveyheinz@shaw.ca
Copyright © 2000, 2001 by Harvey D. Heinz