||I have been fascinated by numbers, and especially
number patterns, since grade school. This site is my testament to that
fact, and my wish to share the wonders of numbers!
there is number, there is beauty.
__ Proclus (410-485 A.D.)
This site is best viewed at a window width of 1040 pixels.
May 19, 2012
created a new DVD, the Magic Square Omnibus.
This is an archive of Magic Hypercube material to date.
After initial distribution,
there are only a small number of these DVDs still available.
There is no cost for them except for shipping and handling.
Details and order buttons
March 22, 2013
A new page !
- Update 2013
developments - Contributors to Magic Tesseract theory - The 5-D
has multiple sections, as shown in the left sidebar. Hopefully it will be of interest to middle and high school students and teachers, and
anyone interested in recreational mathematics.
Most of the mathematics is simple arithmetic, but the many
illustrations are meant to demonstrate the beauty of number patterns. The
most recent section, Magic Tesseracts, is meant to show the relationship
between dimensions. I also show a history of the development of
magic squares, cubes, tesseract, etc.
More on the history of this collection of web pages is
My policy regarding credits on this site is
|Because these pages are written using Microsoft FrontPage,
they are best viewed using Internet Explorer. Formatting suffers somewhat
in FireFox and some other browsers.
||This WWW site is about numbers and the
patterns that can be made from them.
||Most patterns shown here should be
understandable to anyone with about grade 5 math but will hopefully
be of interest also to persons with advanced education..
The section on Magic Stars is
mostly original work & includes material on Orders 5 to 14, a total
of 30 patterns.
||This site represents a very
small proportion of the material I have in my notes. I hope to be
adding to it frequently so please stay tuned.
The true spirit of
delight…is to be found in the mathematics as surely as in poetry.
Bertrand Russell (1872-1970)
||To share my love of the
subject with others.
||To demonstrate that
mathematics can be enjoyed by persons regardless of their education
||To further the appreciation of
mathematics and the understanding of number relationships.
||Who will enjoy this site?
Anyone who loves mathematics in general and numbers in
Teachers looking for enrichment material for their math classes.
||Who designed the patterns?
Probably most of these patterns have been around for many years
and the original author is unknown. Some are of recent origin, and
if the author is known has been credited here. And some are of my
own original design (at least as far as I know).
Most of the Magic Star patterns and
material shown here are my work.
||Who am I?
I am a retired bookbinder and have no training in mathematics
beyond high school.
I have been fascinated by number patterns and have been collecting
them since I was a teenager.
For the last several years I have been researching magic stars and
have made many interesting discoveries.
More information about myself and my family are on my
(Also more Magic Stars & Magic Squares)
Since about 2002 I have been concentrating on magic hypercubes
(squares, cubes, tesseracts, etc.)
||Who are you?
Presumably, because you are looking at this site, you too are
interested in recreational mathematics.
Help explore the mysteries of magic stars. So far, I have been
concentrating mostly on the relationships between the different
orders. Aside from order-6, very little is known about the features
of the individual orders.
If you too find this subject interesting, I would love to hear from
Tell me about yourself, your special interests, and your favorite
A few pages of this collection were first
posted to Geocities in March 1998 as
The title of the Home page until this last posting was Magic
Squares, Stars, & Other Number Patterns.
the years the collection grew in size and became www.geocities.com/~harveyh/. On
Oct. 14/09 the entire site has been moved as is, to this new location, because
Geocities has closed it's doors.
December, 2007 Note: Much of
this Introduction section is now dated. In recent years my interests have
concentrated mostly on Magic hypercubes, resulting in a new site at http://members.shaw.ca/hdhcubes/, and more recently a tesseract site
July 2009 Note: Because this site was developed over more
then a decade, the material tends to be scattered over multiple pages.
Rather then rewrite pages (maybe repeatedly), I have attempted to handle
the problem with links between articles on various pages and with
addendums added to original pages.
November, 2010 Note:
In consolidating the three sites into one, I have retained this same
policy, with only minor rewriting or reorganizing. All 3 original site are
at one location now , with improved navigation and consistent formatting.
The above two sites (hdhcubes and tesseracts) are now redundant and will
eventually be removed. They were required originally because I did not
have the required memory capacity to combine all 3 as one unit.
Two sections, Magic Stars, and Number
Patterns, are actually off the subject of Magic Hypercubes.
However, because these sections were prominent parts of the original site,
I have included them on this new consolidated site.
My policy on all the pages of this WWW site
If I know of only one source for a pattern, acknowledge it (if possible,
obtain permission to use it).
If I have multiple sources for a pattern with no indication of the
original source, consider it public domain.
Consequently, if a pattern has no author
indicated, I obtained it from multiple locations, or it is my own
If you see a pattern on these pages that you feel you should receive
credit for, please let me know the details, so I may reconsider my