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!

Wherever there is number, there is beauty. __ Proclus (410-485 A.D.)

  This site is best viewed at a window width of 1040 pixels.

June , 2013

 I have a 785 book recreation math library I would like to give away.

This is now donated

Thanks to University of Alberta
Meta Development Special Materials Unit
Special Thanks to John Wright, Marlys Chevrefil & Regina Landwehr


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This site 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 here.
My policy regarding credits on this site is here.

Because these pages are written using Microsoft FrontPage, they are best viewed using Internet Explorer. Formatting suffers somewhat in FireFox and some other browsers.


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This WWW site is about numbers and the patterns that can be made from them.

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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..


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The section on Magic Stars is mostly original work & includes material on Orders 5 to 14, a total of 30 patterns.


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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.

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The true spirit of delight…is to be found in the mathematics as surely as in poetry.
__ Bertrand Russell (1872-1970)

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To share my love of the subject with others.

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To demonstrate that mathematics can be enjoyed by persons regardless of their education level.


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To further the appreciation of mathematics and the understanding of number relationships.

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Who will enjoy this site?
Anyone who loves mathematics in general and numbers in particular.
Teachers looking for enrichment material for their math classes.

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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.


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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 Personal Home-page.
(Also more Magic Stars & Magic Squares)
Since about 2002 I have been concentrating on magic hypercubes (squares, cubes, tesseracts, etc.)


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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 you.
Tell me about yourself, your special interests, and your favorite number patterns.

History of this site

A few pages of this collection were first posted to Geocities in March 1998 as www.geocities.com/CapeCanaveral/Launchpad/4057/.
The title of the Home page until this last posting was
Magic Squares, Stars, & Other Number Patterns.

Over 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.

These (and other) early pages may be seen by going to the Internet Archive Wayback Machine.

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 at http://members.shaw.ca/tesseracts/.

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.

All about Credits

My policy on all the pages of this WWW site is:
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 composition.
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 acknowledgment.

Knot 138

About 2000


Jan. 2001


This page was originally posted May 1998
It was last updated June 21, 2013
Harvey Heinz   harveyheinz@shaw.ca
Copyright © 1998-2009 by Harvey D. Heinz