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 (410-485 A.D.)
|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.|
|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/|
|A set of magic squares constructed by Walter Trump. Posted July 2008.|
|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 Knight-tours, March/09 The Unfolded Tesseract
|Dec. 2002 Posted 11 pages on magic cubes to a new site. This site has now grown to 45 pages (June/09).|
Magic Square Lexicon : Illustrated is now in it's second print run!
And now a free PDF version of the first one-quarter of the book.
|A brief introduction to number patterns and these pages.|
|The door to a group of pages displaying and talking about magic squares|
|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.
|More then 160 books, chapters of books or papers dealing with magic squares, etc.|
|Some of my Word, Excel and Basic program files.|
|Approximately 125 terms related to magic squares, cubes, tesseracts, stars, etc.|
|A hodge-podge of miscellaneous patterns from my collection.
Included are number patterns, interesting numbers, magic graphs, etc.
|My policy on these pages, about giving credit where credit is due.|
|Links to other Magic Square, Magic Star and recreational mathematics web sites.|
Shows the organization of this site, complete with direct links to over
|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
|The true spirit of delight is to be found in the mathematics as surely as in poetry.-- Bertrand Russsell (1872-1970)|
|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 Home-page.
(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 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.
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
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, pan-2-n-agonal) 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.
Anti-Magic 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(n2-1)
Harry White has a new site (March 2009) on Bordered Magic Squares. He has computed the number of these up to order-14.
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.luo-shu.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 cut-the-knot 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 digit-related-numbers.
Charles-É. 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 Squares-2 Material from REC Unusual Magic Squares John Hendricks - Cubes Prime Number Magic Squares Quadrant Magic Squares Order-13 Quadrant Magic Squares Order-17 Quadrant Magic Squares Type 2 Order-3 Magic Squares Anti-magic Squares Self-similar Magic Squares Most-perfect Magic Squares Most-perfect Bent diagonal magic squares Magic square Models Transformations & Patterns More Order-4 Transformations Transformations Summary Fellows Transformations Order-4 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 3-D Polygons & Graphs Magic Knight Tours Compact-Magic Squares Ultra-magic Squares Magic square update Magic Stars Magic Star Definitions Magic Star Examples Magic Star Examples - 2 Big Magic Stars Order-5 Magic Stars Order-6 Magic Stars Order-6 Solution List H. E. Dudeney Features Order-7 Magic Stars Order-8 Magic Stars Order-9 Magic Stars Order-10 Magic Stars Order-11 Magic Stars Prime Number Magic Stars Prime Number Magic Stars - 2 Unusual Magic Stars Isomorphic-like magic Stars Magic 9x5 Hexagrams 3-D 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 Self-similar Magic Cubes Magic Cubes - Pan and Semi-pan Unusual Magic Cubes Most-perfect cubes Order 16 perfect cubes Magic Cube Bibliography Cube Downloads Summary of this Magic Cube Site Cube Update-1 Cube Update-2 Cube Update-3 Cube Update-4 Cube_Update-5 Cube_Timeline
Magic Tesseracts - Introduction (Shaw server- but connected by Button Bar) Magic Hypercube Overview Hypercube Representations Hypercube Representations-2 Order 3 Magic Tesseracts Hypercube Aspects Hypercube Classes Associated Hypercubes Hypercube Math More Tesseracts Hypercube Cross-stitch 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 firstname.lastname@example.org
This page last updated October 31, 2009
Copyright © 1998, 1999, 2000, 2001, 2002 by Harvey D. Heinz