I hope you enjoy these examples from my collection of number patterns.
This site has three sections, with pages on magic squares, magic stars (a lot of original material) and miscellaneous number patterns. This site should be of interest to middle and high school students and teachers, and anyone interested in recreational mathematics.
Wherever there is number, there is beauty. __ Proclus (410485 A.D.)
Moved to magicsquares.net 
A few pages of this collection were first posted to Geocities in March 1998 as www.geocities.com/CapeCanaveral/Launchpad/4057/. 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 is closing it's doors.  
Magic Square Update 
Oct. 2009. 3 new types. Normal squares just a subset. Postage stamp m.s., etc.  
Magic Squares, Magic Stars & Other Patterns  June 2009 Thanks to Ed Pegg, this geocities site is now mirrored on http://recmath.org/  
Ultramagic Squares 
A set of magic squares constructed by Walter Trump. Posted July 2008.  
Magic Tesseracts 
Nov. 2007 All about magic tesseracts. A new site (because of space)
consisting of 11 pages. Also discusses the relationships between hypercubes of different dimensions. New pages: October//08 Knighttours, March/09 The Unfolded Tesseract 

Magic Cubes 
Dec. 2002 Posted 11 pages on magic cubes to a new site. This site has now grown to 45 pages (June/09). 
The
Magic Square Lexicon : Illustrated is now in it's second print run!
And now a free PDF version of the first onequarter of the book.
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Introduction 
A brief introduction to number patterns and these pages. 
Magic Squares 
The door to a group of pages displaying and talking about magic squares 
Magic Stars 
I have found the total basic solutions for each order from 5 to 11 and
most for orders 12, 13 and 14. On this page I present some results of this study. Also . . . A new definition for magic stars. Examples of all orders from 5 to 14, a total of 30 different patterns (graphs). All minimum and consecutive solutions for orders 5, 6, 7, 8 prime magic stars Interesting comparisons between the different orders. 
Bibliography 
More then 160 books, chapters of books or papers dealing with magic squares, etc. 
Downloads 
Some of my Word, Excel and Basic program files. 
Glossary 
Approximately 125 terms related to magic squares, cubes, tesseracts, stars, etc. 
Other Number Patterns 
A hodgepodge of miscellaneous patterns from my collection. Included are number patterns, interesting numbers, magic graphs, etc. 
All about Credits 
My policy on these pages, about giving credit where credit is due. 
Similar web sites 
Links to other Magic Square, Magic Star and recreational mathematics web sites. 
Site Map 
Shows the organization of this site, complete with direct links to over
70
pages. 
Talk to me. . . 
Suggestions, criticism, share your favorite number patterns, etc. I would really appreciate any comments you wish to make in regard to these pages, number patterns in general and magic stars in particular, or for that matter, any aspect of recreational mathematics. 
December, 2007 Note: This page was originally posted in 1998. 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 recently the tesseract site mentioned above.
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 Russsell (18721970)  
To share my love of the subject with others.  
To demonstrate that mathematics can be enjoyed by persons regardless of their education level.  
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 particular. 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 Personal Homepage. (Also more Magic Stars & Magic Squares) 

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 order6, 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. 
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.
John R. Hendricks
(1929  2007) still has a website showing Perfect & Inlaid magic tesseracts, as well as
other math topics.
Aale de Winkel is compiling an
Encyclopedia
of magic terms, which is well worth visiting.
Christian Boyer has
constructed tetramagic and pentamagic squares. His site has much information on
multimagic squares and cubes.
Mutsumi Suzuki's
excellent MAGIC SQUARES is now back  hosted by MathForum
Dwane Campbell
has a comprehensive site on Perfect (Nasik, pan2nagonal) magic
hypercubes. He includes generator programs for these forms.
Walter
Trump has a several sites dealing with all aspects of magic hypercubes.
He also discusses counting.
Abhinav Soni has a new site on
magic cubes that features a hyper magic cube generator.
Mitsutoshi Nakamura also has a lot of material and
original research on his cubes site. Also, an excellent page on hypercube
definitions.
Kanji Setsuda has a large site and much information on magic squares. His English pages
are here.
Eric W. Weisstein's Magic Squares
 part of Eric's Treasure Trove Of Math, a very comprehensive work
Francis Gaspalou
has an excellent site dealing with methods and tools for enumeration of magic
squares.
Magic Squares by "Grog"  theory of
Pandiagonal magic squares. Also a good history of magic squares.
Suzanne Alejandre: Magic
Squares  this attractive page presents magic squares as a way of teaching math
Robert W. Wilke's Nested Magic
Squares  simple inlaid Magic squares. Samples. Some theory.
AntiMagic Squares by John Cormie
& Vaclav Linek presents an extensive investigation of this subject.
saMagicSquares is a magic squares
generating program written by Richard W. Bogosian.
Charles Kelly has a Java applet to
generate magic squares and hypercubes.
Simon
Whitechapel has solutions for 1 pattern of each order magic star from 15 to 20. Also
articles on other math subjects.
Cambridge University has an interesting site on Secondary School Math Enrichment.
Paul C. Pasles has pages on Franklin and
other OLD magic squares.
Mark Swaney has a detailed
history of magic squares
.
Mark Farrar's page on
magic squares includes several applets and a subscription link to a
magic squares group.
To see what can be done with art and
magic squares, visit Paul Heimbach's Web site.
G. D. Mutch's
Natural
Matrix Law is a large site which discusses practical (?)
applications of magic squares.
Edward Gutierrez has a new site where he
squares similar to associated, but with center cell containing 1/2(n^{2}1)
Harry White has a new site (March 2009) on
Bordered Magic Squares. He has computed the number of these up to
order14.
Magic Squares Newsgroup at
http://uk.groups.yahoo.com/group/magicsquares/
Magic Cubes Newsgroup at
http://groups.yahoo.com/group/magiccubes/
For magic Squares of Luo Shu format, see Dr. Robert Dickter's
http://www.luoshu.com/
Arie Breedijk has a useful
site containing many methods of magic square construction.
The Math Forum  The premier source on the Web for
educational mathematics. All about math, for the student or hobbyist
Eric's Treasure Trove of Mathematics  covers
a very wide range of material  a big site
Patrick De Geest's World of Numbers
is a very attractive and informative site
Carlos B. Rivera's site, Prime Puzzles and Problems, has lots of food for thought
Mike Keith – has lots of good
material on interesting numbers
Keven Brown  has a great site on a
variety on mathematic subjects.
Harry J.Smith's Fun With Mathematics
 a
variety of programs and subjects on recreational mathematics
Dr. Michael Ecker's Recreational and
Educational Computing newsletter about recreational mathematics and computing
Ed Pegg Jr.'s http://www.mathpuzzle.com has a
great sellection of puzzles and lots of recreational math links
Alexander Bogomolny's cuttheknot large site
deals with many math subjects and has almost 2000 links
Monty Phister's site at http://gnarlymath.com contains
puzzles, games, stories, etc to promote enjoyment of mathematics
For a list of all PPDI's in bases 2 to 10, visit Dr.
Lionel E. Deimel's site
Chris Caldwell has a large site dealing with Prime numbers as
http://primes.utm.edu/
G. L. Honaker, Jr 's & Chris Caldwell's Prime
Curios page has many fascinating facts about individual prime #
A great mathematics site for students is http://www.aaamath.com/
Charles Ashbasher's site has information about the Journal of Recreational Mathematics.
The World of Trotter Math parades
the work of dedicated mathematics teacher Terry Trotter.
Shyam Sunder Gupta discusses RARE and
EPORNS numbers (and other numbers).
Walter Schneider has an informative site dealing with digitrelatednumbers.
CharlesÉ. Jean has a good Dictionary of
recreational mathematics (in French).
A prime spiral arranged as a circle is thoroughly discussed and illustrated at
Rom Sacks
http://www.numberspiral.com/
Math for Kids at
http://www.allmath.com is an entry point to many web sites with
interesting mathematical content.
David Singmaster's source lists on Recreational Mathematics at
www.g4g4.com/MyCD5/SOURCES/singmaterial.htm
Magic Star, Squares, & Other Number Patterns (Geocities and Recmath servers) Magic Squares A Deluxe Magic Square More Magic Squares More Magic Squares2 Material from REC Unusual Magic Squares John Hendricks  Cubes Prime Number Magic Squares Quadrant Magic Squares Order13 Quadrant Magic Squares Order17 Quadrant Magic Squares Type 2 Order3 Magic Squares Antimagic Squares Selfsimilar Magic Squares Mostperfect Magic Squares Mostperfect Bent diagonal magic squares Magic square Models Transformations & Patterns More Order4 Transformations Transformations Summary Fellows Transformations Order4 Lists Order4 #1 to 200 Order4 #201 to 400 Order4 #401 to 600 Order4 #601 to 880 Pandiagonal 5x5 Franklin squares Multimagic Squares Perimeter Magic Triangles Perimeter Magic Polygons >k=3 Magic 3D Polygons & Graphs Magic Knight Tours CompactMagic Squares Ultramagic Squares Magic square update Magic Stars Magic Star Definitions Magic Star Examples Magic Star Examples  2 Big Magic Stars Order5 Magic Stars Order6 Magic Stars Order6 Solution List H. E. Dudeney Features Order7 Magic Stars Order8 Magic Stars Order9 Magic Stars Order10 Magic Stars Order11 Magic Stars Prime Number Magic Stars Prime Number Magic Stars  2 Unusual Magic Stars Isomorphiclike magic Stars Magic 9x5 Hexagrams 3D Magic Stars Trenkler Stars Magic Star Puzzles Star Updates Simon Whitechapel Jon Wharf Andrew Howroyd Number Patterns Prime Patterns More Prime Patterns Narcissistic Numbers Palindromes Glossary Bibliography Book for Sale Downloads
Magic Cubes  Introduction (Shaw server but connected by Button Bar) Magic Cubes  The Basics Magic Cube  Definitions Perfect Magic Hypercubes Magic Cubes  the Road to Perfect The Early Cubes A. H. Frost's Magic Cubes F. A. P. Barnard's Magic Cubes Magic Cubes  Order 3 Magic Cubes  Order 4 Magic Cubes  Order 5 Magic Cubes  Order 6 Magic Cubes  Order 7 Magic Cubes  Order 8 Magic Cubes  Order 9 Magic Cubes  Order 10 Magic Cubes  Order 11 Magic Cubes  Order 12 Magic Cubes  Order 13 Arnoux's Perfect Cube Arnoux Patterns Modulo Magic Cubes Multimagic Cubes Monster Cubes Boyer's Bimagic 16 Cube Boyer's Bimagic 32 Cube Magic Cube Groups Prime Number Magic Cubes Magic Cubes  Multiply Composition Magic Cubes Hendricks Inlaid Magic Cubes The Heinz X6 Magic Cube Selfsimilar Magic Cubes Magic Cubes  Pan and Semipan Unusual Magic Cubes Mostperfect cubes Order 16 perfect cubes Magic Cube Bibliography Cube Downloads Summary of this Magic Cube Site Cube Update1 Cube Update2 Cube Update3 Cube Update4 Cube_Update5 Cube_Timeline
Magic Tesseracts  Introduction (Shaw server but connected by Button Bar) Magic Hypercube Overview Hypercube Representations Hypercube Representations2 Order 3 Magic Tesseracts Hypercube Aspects Hypercube Classes Associated Hypercubes Hypercube Math More Tesseracts Hypercube Crossstitch Knight Tours in Higher Dimensions The Unfolded Tesseract
Thanks for the visit and I hope to see you again soon.
Please send me Feedback about my Web site!
Harvey Heinz harveyheinz@shaw.ca
This page last updated
October 31, 2009
Copyright © 1998, 1999, 2000, 2001, 2002 by Harvey D. Heinz