
The following bibliography consists of books, chapters from books, and
articles published during the 20^{th} century, that deal with
magic squares, cubes, stars, etc. Because it contain only material that I
am personally acquainted with (except for this first section), it is
obviously not complete. However, it does contain about 300 items.
For 18^{th} and 19^{th} century books on the
subject see
Early Books on Magic Squares William L. Schaaf
JRM:16:1:198384:16
For a list of articles published before about 1970 see
A Bibliography of Recreational Mathematics (4 volumes),
published. by National Council of Teachers of Mathematics, 1978
For a list of articles published since about 1970 see
Vestpocket Bibliographies No. 12: Magic Squares and Cubes....William L.
Schaaf JRM:19:2:1987:8186
Some books on magic squares published prior to that time are
[1]
Agrippa 
1510 
De Occulta Philosophia (II, 42) 1510 
Bachet 
1624 
Problems plaisans et delectables 1624 
Prestet 
1689 
Nouveaux Elemens des Mathématiques 1689 
De la Loubere 
1693 
Relation du Royaume de Siam 1693 
Frenicle 
1693 
Des Quarrez Magiques. Acad. R. des
Sciences 1693
(this is a posthumous paper, not a book)

Ozonam 
1697 
Récréations Mathématiques 1697 (3 volumes)
This book is now available at Cornell Univ. Digital
Math Library 
Violle 
18378 
Traité complet des Carrés Magiques 
[1] Falkener, Edward, Games Ancient and Oriental and
How to Play Them, Dover Publ., 1961, 0486207390,
page 269

Complete Books
Andrews, W. S., Magic Squares & Cubes,
Open Court, 1908, 193+ pages.
The first 188 pages of edition 2 is almost exactly the same as this.
Differences are:
 Pages in the two editions are identical to page 128.
 Section on ‘Math Study’ is reduced from pp 129155 to
129145 in edition 2.
 Section on ‘M. S. and Pythagorean’ is almost
identical (pp 156172 and 146162.
 Section on ‘Some Curious…’ is expanded from pp 173184
to 163178.
 Section on ‘Notes on Various…’ is expanded slightly from
pp 185193 to 178188 in edition 2.
Andrews, W. S., Magic Squares & Cubes, 2^{nd}
edition, Dover Publ. 1960, 419+ pages .
This is an unaltered reprint of the 1917 Open Court Publication of the second
edition. It consists of essays by different authors, first published in The
Monist from 1905 to 1916. The first 188 pages are almost identical to
edition 1 published in 1908 (see above).
Arnoux, G., Arithmetique graphique – les espaces
arithmetiques hypermagiques, GauthierVillars, 1894,175+ pages. (French).
Lots of theory with methods of construction.
Mention is made of
a paper containing 26 handwritten pages with a perfect (new definition) magic
cube.
Cube Diabolique de DixSept,
was deposited in the Académie des Sciences, Paris, France, April 17, 1887.
Benson, W. &
Jacoby, O., New Recreations with Magic Squares, Dover Publ., 1976,
0486232360
This book is a serious attempt to bring the theory of magic squares up to date
(1976). The authors present a new method of cyclically developing magic squares.
They include a listing of all 880 4 by 4 magic squares. A chapter shows how to
generate all 3600 5x5 pandiagonal magic squares.
Benson, W. &
Jacoby, O., Magic Cubes: New Recreations, Dover Publ., 1981,
0486241408
This book provides a valuable contribution to the literature, including an early
perfect order8 magic cube..
Calter, Paul,
Magic Squares, T. Nelson and Sons, 1977,0840765460
A mathematical detective story with no actual connection to magic squares. but
includes mathematical problems.
Candy, Albert
L., Pandiagonal Magic Squares of Prime Order, selfpublished, 1940
A small hardbound book with much theory on the subject.
Cazalas,
Emile, A travers les hyperspaces magiques (Through Magic Hyperspace).
Sphinx, 1936, 19 pages (French).
Danielsson,
Holgar, Printout of an Order25 Bimagic Cube, Selfpublished, 2000,
36 pp plus covers, flatstitched, 8.5 x 11
A nicely formatted and printed graphical version of John Hendricks Bimagic Cube
of Order 25.
Descombes,
Rene, Les Carrés Magiques (Magic Squares), Vuibert, 2000,
2711752615, 494 pages. (French)
Farrar, Mark S.,
Magic Squares, selfpublished 1996. 72 pp plus 34 pages of appendices.
Analyzes order3, 4 and 5. Gives lists of combinations that sum correctly.
Slanted towards presenting magic squares as entertainment.
Fitting, Prof. Dr. F. , Panmagische Quadrate
und magische Sternvielecke, Panmagic squares and magic stars, 1939,
70 pages. Pages 52 to 70 are on magic stars including lots of diagrams.
Fults, John Lee,
Magic Squares, Open Court Publ., 1974, 0875481973
This book contains a wealth of information on all types of magic squares. It is
written as a text book and includes exercises at the end of each chapter.
Heinz, H.D. and
Hendricks, J. R., Magic Square Lexicon: Illustrated. Selfpublished,
2000, 0968798500.
239 terms defined, about 200 illustrations and tables, 171 captioned.
Hendricks, John
R., The Magic Square Course, Unpublished, 1991, 554 pages 8.5 " x 11"
binding posts.
Written for a high school math enrichment class he conducted for 5 years.
Hendricks, John
R., A Magic cube of Order10, Unpublished, 1998 23 pages 8.5 " x 11"
flat stitched.
…With an inlaid cube of order6 and adorned with 12 inlaid magic squares of
order6.
Hendricks, John
R., Magic Squares to Tesseract by Computer, Selfpublished, 1998,
0968470009
212 pages plus covers, 8.5" x 11" spiral bound, 100+ diagrams.
Lots of theory and diagrams, new methods and computer programs. 3 appendices.
Hendricks, John
R., Inlaid Magic Squares and Cubes, Selfpublished, 1999,
0968470017
206 pages plus covers, 8.5" x 11" spiral bound, 100+ diagrams.
Lots of theory and diagrams. Includes a list of 46 mathematical articles
published in periodicals by the author.
Hendricks, John
R., All ThirdOrder Magic Tesseracts, Selfpublished, 1999,
0968470025, 36 pages plus covers, 8.5" x 11" flat stitched, 60+ diagrams.
Some theory. Lots of diagrams.
Hendricks, John
R., Perfect nDimensional Magic Hypercubes of Order 2n,
Selfpublished, 1999, 0968470041. 36 pages plus covers, 8.5" x 11" flat
stitched, some diagrams.
Theory with examples for a cube, tesseract and 5D hypercube.
Hendricks, John
R., BiMagic Squares of Order 9, Selfpublished, 1999, 0968470068.
14pp + covers, 8.5" x 11" flatstitched..
A method of generating these squares using equations and coefficient matrices.
Hendricks, John
R., Bimagic Cube of Order 25, SelfPublished 2000, 18pp plus covers,
flatstitched 8.5 x 11.
This remarkable cube is presented in equations. A short computer program
(listed) displays the number in any specific location..
Hugel, Dr.
Theod., Das Problem der magischen Systeme, Neustadt a. D. H., 1876 48 pp +
12 plates.
This book is written in German. It contains a lot of mathematics. The plates
show a large number of magic squares of different orders and types as well as
magic cubes of orders 3, 5 and 8.
The book is available online or custom printed hardcopy from Cornell University
at
http://www.math.cornell.edu/~library/reformat.html
Kelsey, Kenneth,
The Cunning Caliph, Frederick Muller, 1979, 0584103670
This is one of the five books (the first one) that make up The Ultimate Book of
Number Puzzles.
Kelsey, Kenneth,
The
Ultimate Book of Number Puzzles,
Cresset Press, 1992, 0880299207, 522 pages.
This is a combination of 5 books ( four by K Kelsey & the last one by D. King),
all published in Great Britain 19791984 by Frederick Muller Ltd.
It consists of numerical puzzles in the form of magic squares, cubes, stars,
etc. No theory, but lots of examples (some quite original) and lots of practise
material.
Lehmann, Max Bruno, Der geometrische Aufbrau
Gleichsummiger Zahlenfiguren (The Geometric Construction of Magic Figures),
1875, xvi+384 pages.
This book is mostly about magic squares, but includes discussions and examples
of magic cubes and magic stars.
Moran, Jim,
The Wonders of Magic Squares, Vantage Books, 1982, 0394747984
A large format book that is simply written with little theory, but demonstrates
a large variety of ways to construct magic squares. Contains a forward by Martin
Gardner.
Ollerenshaw, K.
and Brée, D., MostPerfect Pandiagonal Magic Squares, Cambridge Univ.
Press, 1998, 090509106X
The methods of construction and enumeration of these special doublyeven magic
squares.
Philip, Morris,
The Morris Philip magic squares, 1986, vi+26 pages.
Pickover,
Clifford A., The Zen of Magic Squares, Circles and Stars, Princeton
Univ. Press, 2002, 0691070415
400 + pages filed with usual and very unusual magic objects. Lots of
illustrations. Written in Pickover's usual entertaining and informative style.
Scheffler, Hermann, Die Magischen Figuren
(Magic Figures), Martin S, 1968, 112 pages. (German)
Simpson, Donald
C., Solving Magic Squares, 1^{st} Books, 2001, 0759604282,
102pp.
Various methods are shown for solving the different orders of magic squares.
Swetz, Frank J.,
Legacy of
the Luoshu,
Open Court, 2002, 0812694481, 214pp
Discusses the order 3 and other magic squares in early China, India, Arab
countries and the Western world. It includes a large bibliography of references.
Violle, Par B, Traité complet des Carrés Magiques,
1837, 1000+ pages (French). About 100 pages on magic cubes. It is available on
the Internet at
http://gallica.bnf.fr/ as scanned pages. A selected page may be viewed or
the entire book may be downloaded.
Weidemann,
Ingenieur, Zauberquadrate und andere magische Zahlenfiguren der Ebene und
des Raumes, Oscar Leiner, 1922, 83 pages. Translated title is Magic
squares and other plane and solid magic figures. (German)This book contains
many examples of magic squares, cubes, and geometric figures.
Partial
Books
The following books have chapters or sections dealing with magic squares (and
related subjects).
Ahl, David H.,
Computers in Mathematics, Creative Computing Pr., 1979, 091668816X
Contains some theory and Basic language programs to generate magic squares.
Pages 111117
Berlekamp, E.,
Conway, J. and Guy, R.,
Winning Ways vol. II, Academic Press, 1982, 01120911027
Original material on order4 magic squares. Also shows a tesseract with magic
vertices. Pages 778783.
Czepa, A., Mathematische Spielereien
(Mathematical Games), Union Deutsche, 1918, 140 pages.
(Old German script). Many magic objects in this small format book.
Dudeney, H. E.,
536 Puzzles & Curious Problems, Charles Scribner's Sons, 1967,
684717557
This material was first published posthumously in 1926 and 1931 Unusual problems
and some theory for magic squares, stars and other objects. pp 141  149 and
344  354.
Dudeney,
H. E., Amusements in Mathematics, Dover
Publ., 1958, 0486204731. Originally published in 1917. Order 4 classes
Subtraction, multiplication, division, domino, etc. List of first prime # magic
squares, etc. Pages 119127 and 245247.
Falkener,
Edward,
Games Ancient
and Oriental and How to Play Them, Dover Publ., 1961, 0486207390
First published by Longmans, Green & Co. in 1892, this book contains the
original text with no changes, except for corrections. A comprehensive
discussion of magic squares circa 100+ years ago. Pages 267356.
Fourrey, Emile,
Recréations arithmétiques, (Arithmetical Recreations) 8^{th}
edition, Vuibert, 2001, 2711753123, 261+ pages. (French). Originally published
in 1899. It includes several magic cubes.
Gardner, Martin,
2nd Scientific American Book of Mathematical Puzzles and Diversions,
Simon and Schuster, 1961, 6112845
Diabolic hypercube (tesseract), diabolic donut, some history, pages 130140
Gardner, Martin,
Incredible Dr.
Matrix, Scribners, 1967, 068414669X
Antimagic, multiplication & division, pyramid, etc. Pages 21, 47, 211, 246
Gardner, Martin,
Mathematical Carnival, Alfred Knopf, 1975, 0394494067
Hypercubes, pages 4154. Magic Stars, pages 5565
Gardner, Martin,
Mathematical Puzzles & Diversions, Simon & Schuster, 1959, 599501
Chapter 2, Magic With a Matrix, pages 1522.
Gardner, Martin,
New Mathematical Diversions, Simon and Schuster, 1966, 671209132
Euler's spoilers order10 Graeco Latin squares, order4 playing card magic
square. Pages 162172
Gardner, Martin,
Penrose Tiles to Trapdoor Ciphers, Freeman, 1989, 071671986X
Alphamagic, smith numbers, 3x3 properties, pages 293305
Gardner, Martin,
Scientific American Book of Mathematical Puzzles and Diversions,, Simon
and Schuster, 1959, 599501
Using magic squares for magic tricks, pages 1522.
Gardner, Martin,
Sixth book of Mathematical Games, Charles Scribner's Sons, 1963,
0684142457
Magic hexagons, pages 2325. Consecutive prime s. (using #1) pages 8687.
Gardner, Martin,
Time
Travel & Other Mathematical Bewilderments,
Freeman Publ., 1988, 071671924X
First published enumeration of Order5 magic squares and information about
order8 magic cubes. Gardner refers to ‘perfect’ magic cubes. This type of cube
is now called a myers cubes (the new perfect magic cubes are a much higher
class). Chapter 17 Magic Squares & Cubes. Pages 213226.
Note that Gardner erroneously stated that all 5 x 5 magic squares with 13 in the
center are associated.
Goodman, A. W.,
The Pleasures of Math, Macmillan, 1965, 224 pages
Chapter 3, pp 40  57) are on magic squares.
Heath, Royal Vale,
Mathemagic, Dover Publ., 1953.
The author copywrited this material in 1933. Some unusual patterns. Pages
87123.
Hunter, J. & Madachy,
J.,
Mathematical Diversions, Van Nostrand, 1963,
Theory of magic squares includes a simple method to produce bimagic squares.
Pages 2334.
Kraitchik, Maurice,
Mathematical Recreations, Dover Publ., 1953, 539354. (orig publ.
W.W.Norton, 1942)
Construction methods, multimagic, GreacoLatin, border, order4 theory,
definitions, etc. Pages 142192
Langman, Harry,
Play Mathematics, Hafner Publishing Co, 1962
Pages 70 to 76 are on magic squares and an order 7 pandiagonal magic cube.
Lucas,
Edouard, L’Arithmétique amusante (Amusing Arithmetic), GauthierVillars,
1895,266+ pages. (French). Fermat magic cube. Looks like an interesting book,
but only 1 magic cube, Fermat’s order 4.
Madachy, Joseph
S., Mathematics on Vacation, Thomas Nelson Ltd., 1968, 171470990
A good discussion of magic, antimagic, heterosquare, talisman, etc squares,
pages 85113.
Madachy, Joseph
S.,
Mathematical Recreations,
Dover Publ., 1979, 0486237621.
A pageforpage copy of the above Mathematics on Vacation.
Meyer, Jerome
S., Fun With Mathematics, World Publ., 1952, 528434
A good discussion of bigrades and upsidedown magic squares of order4. Pages 47
to 54.
Olivastro,
Dominic, Ancient Puzzles, Bantam Books, 1993, 0553372971
On a Turtle Shell, pages 103125, discuss the Lo Shu ,Pandiagonal, Franklin and
composite magic squares. Also magic graphs. However, he erroneously states that
no one has yet discovered a magic tesseract.
Ozanam, Jacques (16401717), Recreations in the
Science and Natural Philosophy, 1697. Enlarged by Jean Montucla about
1768. Translated into English by Dr. C. Hutton in 1803. Finally revised by
Edward Little in 1844. This book is 826 pages but only Part 1 (113 pages) is
concerned with recreational mathematics and only pages 94 to 106 with magic
squares. There is nothing on magic cubes. This book is obtainable over the
Internet from Cornell University Library, Digital Collections at http://historical.library.cornell.edu/math/about.html
Pickover, Clifford A.,
Wonder of Numbers, Oxford Univ. Press, 2001, 0195133420
Chap 101, p 233239 and frontispiece. These few pages have some real gems.
Rouse
Ball, W. & Coxeter, H., Mathematical Recreations & Essays, 12^{th}
Edition, Univ. of Toronto Pr., 1974, 0802061389.
Chapter 7 is on magic squares (pages 189221 in editions 11, 12 and 13).
This classic work was originally published in 1892. H. S. M. Coxeter brought it
up to date with the 1938 publication of the 11th edition, with corrections in
1962 (3927626), the 12th edition in 1974, and edition 13 (Dover, 0486253570)
in 1987 .
NOTE: Edition 10, 1922, has a much different chapter VII, It is at pages
137161, and contains less on magic squares, nothing on magic cubes and more on
magic stars.
Schubert,
Hermann, Mathematical Essays and
Recreations. Translated from German to English by Thomas J. McCormack (1899,
Open Court, 1903. 143+ pages. The chapter on magic squares is on pages 39 to 64.
It includes orders 4 and 5 magic cubes and other magic figures.
This book is obtainable over the Internet from Cornell University Library,
Digital Collections at http://historical.library.cornell.edu/math/about.html
Schubert, Hermann, Mathematische Mussestunden
(Mathematical Pastimes)), 1963 reprint of 1900 work. Sections on various
subjects. pp172176 discuss magic stars. (This section was not in the original
or 1940 reprint).
Schubert, Hermann, Mathematische Mussestunden,
(Mathematical Pastimes), Walter de Gruyter, 1940, 245 pages. Originally
published 1900? The preface was dated 1897. (German). pp 142172 was on magic
squares.
Schubert, Hermann, Mathematische Mussestunden II,
(Mathematical Pastimes II), G.J. Goshen’sche, 1909, 247+ pages. (German). This
book was date stamped Berlin, 12 Nov. 1900! Although one of the keywords was
‘magic cubes’ there were none in this book.
Sperling, Walter, Spiel und Spass furs Ganze
Jahr (Fun and Games for all Years), Albert Muller, 1951, 111 pages. (German)
Not an awful lot on magic cubes. He shows an order 4 block puzzle.
Sperling, Walter, Die Grubelkiste (The
Amusement Chest), Albert Muller, 1953, 162 pages. (German). He shows the same
order 4 that Schubert published.
Singmaster,
David,
MyCD.003, selfpublished 2001. A CD containing 126 of his files on
Recreational mathematics including extensive bibliographies on magic squares
(and other recreational mathematics subjects).
Stein, Sherman K.,
Mathematics: The Manmade Universe, 1963, W. H. Freeman, 637786
Chap. 12, Orthogonal Tables. Discussion of GreacoLatin squares and magic
squares. Pages 155174
Spencer,
Donald D.,
Game Playing with
Computers,
Hayden, 1968, 0810451034
Computer programs and magic square theory. Pages 23107. Card, division, upside
down, composite, prime, subtracting, etc. Pages 209224.
Spencer,
Donald D.,
Game Playing with Basic, Hayden, 1977, 0810451093
Computer programs and magic square theory. Pages 119141.
Spencer,
Donald D.,
Exploring Number Theory With Microcomputers, Camelot, 1989, 0892182490
Computer programs and magic square theory, geometric, talisman, multiplying,
heterosquares, prime, etc. Pages 155180.
Weisstein, Eric W.,
Concise Encyclopedia of Mathematics, CRC Press, 1999, 0849396409
A general mathematical encyclopedia containing more then 14,000 entries so has
many on magic square related subjects. However, some of these terms are
ambiguous or contradictory. No mention of Hendricks modern concise and
comprehensive hypercube classes.
Weisstein,
Eric W.,
Concise Encyclopedia of Mathematics CDROM, CRC Press, 1999, 0849319455
Contains all of the material in the book, plus interactive graphics and both
internal and external hyperlinks.
Games & Puzzles for
Elementary and Middle School Mathematics,
Readings from the
Arithmetic Teacher Published by National Council of Teachers of Mathematics,
1975, 0873530543. Pages 6978, 151156.
Readings for
Enrichment in Secondary School Mathematics,
Bordered Magic Squares.
Published by National Council of Teachers of Mathematics, 1988, 087353252X,.
Pages 195199.
Treasury
of Folklore – Fantasies in Figures, Mathematic Mysteries and Magic, 1965,
newsletter edited by Stanley J. Coleman (Meloc?), 11 legal size typewritten
sheets.
Published
Papers
Abe, Gakuho, Fifty Problems of Magic
Squares, Self published 1950. Later republished in Discrete Math, 127,
1994, pp 313. The last 10 problems deal with magic cubes. It also
includes the Abe order 6 cube.
Adler,
Allen & Li, Shuoyen,
Magic Cubes and Prouhet Sequences, The American Mathematical Monthly,
Vol. 84, No. 8, Oct. 1977, pp. 618627.
They show (with quite a bit of mathematics) several methods of forming
magic squares from smaller order magic cubes.
Agnew, E.,
Two Problems on Magic Squares, Mathematics Magazine, 44, 1971, pp1315.
Ajose, Sunday A.,
Subtractive Magic Triangles, Mathematics Teacher, 76, 1983, pp 346347.
Brian Alspach & Katherine Heinrich, Perfect Magic
Cubes of Order 4m, The Fibonacci Quarterly, Vol. 19, No. 2, 1981, pp 97106
They define a perfect magic cube as one where all the main diagonals sum
to S (we now called these myers cubes). They then site examples of
pandiagonal magic cubes.
AmirMoez, Ali R.,
Isomorphisms on Magic Squares, College Mathematical Journal, 14, 1983, pp
4851.
Anderson, D. L.,
Magic Squares: Discovering Their History and Magic,
Mathematics Teaching in the Middle School, Vol. 6, No. 8, pp.466473
Gabriel Arnoux, Cube Diabolique de DixSept,
Académie des Sciences, Paris, France, April 17, 1887.
26 handwritten pages contain a perfect (new definition) magic cube of order 17.
This cube contains 51 planar, 6 oblique, and 96 2segment oblique, order 17
pandiagonal magic squares.
Thanks to Christian Boyer, who kindly photographed these pages for me (the
Academy would not allow photocopying).
F.A.P. Barnard, Theory of Magic Squares and Magic
Cubes, Memoirs of the National Academy of Science, 4,1888,pp. 209270.
Construction details of the "Frankenstein" cube, described in a lengthy footnote
on pages 244248, are quoted, almost verbatim, in Benson and Jacoby (1981). He
introduces the first (?) normal perfect magic cubes. An order 8 and two order 11
perfect cubes are shown with full information on how they were constructed. He
also shows a magic cylinder and magic sphere.
Christian Boyer, Les cubes magiques, Pour la
Science, Sept. 2003, No. 311, pp 90  95.
A hsitory of magic cubes and a description of his order 8192 quadramagic cube.
Brown, P. G.,
The MAGIC SQUARES of Manuel Moschopoulos, A Translation,
Pure Mathematics Report PM97/22, AMS/01A20/01A75, 32 pages (the original was
written about
1315
A. D.)
Benjamin, A. and
Yasudi, K.,
Magic ‘Squares’ Indeed!, American Mathematical Monthly, 1999,106, pp
152156.
Bona, Miklos,
Sur l'enumeration des cubes magiques, 1993, 316, 633636.
Caldwell, Janet,
Magic Triangles, Mathematics Teacher, Vol. 71, No. 1, 1978, pp. 3942
Carmony, Lowell A.,
A Minimathematical Problem: The Magic Triangles of Yates,
Mathematics Teacher, Vol.70, No. 5, 1977, pp. 410413.
Chen, Yung C. &
Fu, ChinMei,
Construction and Enumeration of Pandiagonal magic squares of Order n from
Step Method, ARS Combinatoria 48(1998) pp. 233244.
Cohen, Martin &
Bernard, John,
From Magic Squares to Vector Spaces,
Mathematics Teacher, Vol. 75, No. 1, Mar. 1982, pp. 76, 77 and 64.
Euler, Leonard, De Quadratis Magicis,
Written in Latin , presented Oct. 17, 1776 to St. Petersburg Academy
This is available in English at
http://front.math.ucdavis.edu/ and search for 0408230
Fellows, Ralph,
Three Impossible Magic Squares,
Mathematical Spectrum, Vol. 23 No. 2, 2000/01, pp. 2833.
Frost, Rev. A. H., Invention of Magic Cubes.
Quarterly Journal of Mathematics, 7, 1866, pp 92102
He describes a method of constructing magic cubes and shows an order 7
pandiagonal and an order 8 pantriagonal magic cube.
Frost, Rev. A. H., Supplementary Note on Magic
Cubes. Quarterly Journal of Mathematics, 8, 1867, p 74
Frost, Rev. A. H., On the General Properties of
Nasik Squares, QJM 15, 1878, pp 3449
Construction of pandiagonal magic squares.
Frost, Rev. A. H., On the General Properties of
Nasik Cubes, QJM 15, 1878, pp 93123 plus plates 1 and 2.
He shows two order 3 and order 4 cubes, and one each of orders 7 and 9, with
method of construction. These cubes (in order) are not magic, disguised order 3,
not magic, pantriagonal, pantriagonal and perfect.
Frost, Rev. A. H.,
Description of Plates 3 to 9, QJM 15, 1878, pp 366368 plus plates 3 to
9.
Illustrations of a group of 7 interrelated order 7 cubes.
Gerdas,
On Lunda Designs and Associated Magic Squares, College Mathematical Journal,
2000, 31, 182188.
Heath, R. V.,A Magic Cube With 6n^{3}
cells, American Mathematical Monthly, Vol. 50, 1943, pp 288291.
Hendricks, John R.,
The Five and Six Dimensional Magic Hypercubes of Order 3, Canadian
Mathematical Bulletin, Vol. 5, No. 2, 1962,pp. 171189.
Hendricks, John R.,
The Pan4agonal Magic Tesseract, The American Mathematical Monthly, Vol.
75, No. 4, April 1968, p. 384.
Henrich, C.J.,
Magic Squares and Linear Algebra, American Mathematical Monthly, 98,
1991, pp 481488.
House, Peggy A.,
More Mathemagic From a Triangle, Mathematics Teacher, 73, 1980, pp
191195.
Karpenko, Vladimír,
Between Magic And Science: Numerical Magic Squares,
Ambix, Vol. 40, No. 3, 1993, pp. 121128 (Charles Univ., Czech Republic)
Karpenko, Vladimír,
Two Thousand Years of numerical magic squares, Endeavour, New Series,
18,4, 1994, pp147153. No mention of magic cubes.
These 3 papers by Dr. Karpenko are well researched. They contain extensive
references, illustrations and photos.
Karpenko, Vladimír,
Magic Squares: Numbers and Letters, Cauda Pavonis (Univ. of Washington),
Vol. 20, No. 1, 2001, pp 1119.
Kenney, M.,
An Artful Application Using Magic Squares, Mathematics Teacher, Vol.
,75, No. 1, 1982, pp. 8389
Lancaster, Ronald
J.,
Magic Square Matrices, Mathematics Teacher, 72, 1979, pp 3032.
F. Liao, T. Katayama, K. Takaba, On the
Construction of Pandiagonal Magic Cubes, Technical Report 99021, School of
Informatics, Kyoto University, 1999. Available on the Internet at http://www.amp.i.kyotou.ac.jp/tecrep/TR1999.html
They define Pandiagonal Magic Cubes as all orthogonal and diagonal arrays are
pandiagonal magic squares and show 2 order 13 cubes as an example. By the new
definition, these are perfect magic cubes.
They also demonstrate that there are m1 broken pandiagonal magic squares
parallel to each of the 6 oblique pandiagonal magic squares.
Lyon, Betty Clayton,
Using Magic Borders to Generate Magic Squares, Mathematics Teacher, Vol.
77, No. 3, Mar. 1984, pp. 223226.
Manuel Moschpoulos (about 1265 – 1315),
The Magic Squares of Manuel Moschpoulos, Pure Mathematics Report PM97/22,
AMS/01A20/01A75. Translated into English by P.G. Brown (date?) from a French
translation of P. Tannery in 1886. 33 pages. Different methods of constructing
magic squares. No mention of magic cubes.
McClintock, Emory, On the Most Perfect Forms of
Magic Squares,
American Journal of Mathematics, 1897, 19, pp 99120. (Read before the
AMS Apr. 25, 1896). Early research on mostperfect magic squares.
McInnes, S.W., Magic Circles, American
Mathematical Monthly, 60, 1953, pp347350.
Pasles, Paul C.,
The Lost Squares of Dr. Franklin, The American Mathematical Monthly, Vol.
108, No. 6, JuneJuly 2001, pp. 489511.
This well researched paper cites 49 sources and includes a fantastic order 16
pandiagonal magic square.
Planck, C.,
The Theory of Path Nasiks, Printed for private circulation by A. J.
Lawrence, Printer, Rugby, 1905
Reiter, Harold B.,
Problem Solving With Magic Rectangles, Mathematics Teacher, Vol. 79, No.
4, Apr., 1986, pp. 242245.
B. Rosser and R. J. Walker, Magic Squares: Published
papers and Supplement, a bound volume at Cornell University, catalogued as QA
165 R82+pt.14. All papers are very technical. There are NO diagrams. The bound
book contains:
 On the Transformation Group for Diabolic Magic Squares
of Order Four, Reprinted from Bulletin of the American Mathematical Society,
June 1938.
 The Algebraic Theory of Diabolic Magic Squares,
Reprinted from Duke Mathematical Journal Vol. 5, No. 4, Dec. 1939, pp 705728.
Section 6 (pp 727728) has been crossed out.
 A continuation of The Algebraic Theory of Diabolic
Magic Squares on typewritten pages numbered 729 – 753. (This starts with a
new section 6, renamed from ‘conclusion’ to ‘Latin Squares’). Pages 736 to 753
is about diabolic (perfect) magic cubes and points out there are 3m
diabolic magic squares parallel to the faces of the cubes and 6m
diabolic magic squares parallel to each of the diagonal planes.
 Magic Squares, Supplement, on typewritten pages numbered
–2 to 27. Three of the 9 sections are on the subject of magic cubes.
Schwartzman, Steven,
Multiplicative Squares: Magic and Special, Mathematics Teacher, Vol. 80,
No. 1, Jan. 1987, pp. 5154.
Sallows, Lee,
The Lost Theorem, (about the 3x3 square of squares),The Mathematical
Intelligencer, Vol. 19, No. 4, 1997, pp. 5154
Sallows, Lee,
Three Impossible Magic Squares, Mathematical Spectrum, 33, 2000, pp2833.
Sayles, Harry A.,
A Magic cube of Order Six, The Monist, 20, 1910, 299303.
Sayles, Harry A.,
Geometric Magic Squares and Cubes, The Monist, 23, 1913, 631640.
H. A. Sayles, General notes on the Construction
of Magic Squares and Cubes with Prime Numbers,
The Monist, XXVIII, 1918, pp 141158. He shows several order 4 magic squares
with all prime numbers. He also shows an order 3 magic cube that contains 26
primes and 1 composite number.
Schroeppel, Richard,
Appendix 5: The Order 5 Magic Squares, 1973, 116
This is a report of Schroeppels work with enumeration of order 5 magic squares ,
writeup by M. Beeler, mentioned by Gardner in his Scientific American column
Jan. 1976.
Schwartzman, S.,
Multiplicative Squares, Magic and Special, Mathematics Teacher,80. 1987,
pp 5154.
Seimiya, Mathematical Sciences (Japanese)
Magazine Dec. 1977, Special issue on puzzles, p. 4547 orders 9 and 11
perfect magic cubes. Another 10 pages on many magic objects.
Sesiano, Dr.
Jacques,
Islamic Magic Square History, From the author 2002, pp 19.
Swetz, Frank,
Mysticism and Magic in the Number Squares of Old China, Mathematics
Teacher, Vol. 71, No. 1, Jan. 1978, pp. 5056
Swetz, Frank,
If the Squares don't Get You  The Circles Will, Mathematics Teacher,
Vol. 73, No. 1, Jan. 1980, pp. 6772
Trenkler, D &
Trenkler, G.,
Magic squares, Melancholy and the MoorePenrose Inverse, Image, 27, 2001,
pp310.
Trenkler, Marián,
Characterization of Magic Graphs,
Czechoslovak Mathematical Journal, 1983, Vol. 33 ,No.108, pp.435438 (printed in
English)
Trenkler, Marián,
Magic Cubes, The Mathematical Gazette, 82, (March, 1998), 5661.
Trenkler, Marián,
Magic Rectangles, The Mathematical Gazette, 83, 1999, 102105.
Trenkler, Marián,
A Construction of Magic Cubes, The Mathematical Gazette, 84, (March,
2000), 3641.
Trenkler, Marián,
Magic pdimensional Cubes of order n not congruent to 2 (mod 4), Acta
Arithmetica (Poland), 92(2000), 189194.
Trenkler, Marián,
Connections  Magic Squares, Cubes and Matchings, Applications of Modern
Mathematical Methods, Univ. of Ljubljana, Slovenia, 2001, pp. 191199
Trenkler, Marián,
Additive and Multiplicative Magic Cubes., 6th Summer school on
applications of modern math. methods, TU Košice 2002, 2325.
Trenkler, Marián,
Magic Stars, The IIME Journal, vol. 11, No. 10, Spring 2004, pp549554.
Widdis, D. B.,
It’s Magic! Multiplication Theorems for Magic Squares, College
Mathematical Journal, 20, 1989, 301306.
Worthington, John,
A Magic Cube of Six, The Monist,20, 1910, pp 303309.
Articles
in J. Recreational Math.
The following Articles on Magic Squares appear in
Recreational Mathematics
Magazine
I show these as Title, Author, RMM:issue #:date:pages(s)
More Strictly for Squares 
Miscellaneous authors 
RMM: # 5 
Oct. 1961 
p2429 
Add Multiply Magic Squares 
Walter W. Horner 
RMM: # 5 
Oct. 1961 
p3032 
How to Make a Magic Tesseract 
Maxey Brooke 
RMM: # 5 
Oct. 1961 
p4044 
More Strictly for Squares 
Miscellaneous authors 
RMM: # 7 
Feb. 1962 
p1415 
Antimagic squares 
J. A. Lindon 
RMM: # 7 
Feb. 1962 
p1619 
Magic Knight Tours on Square Boards 
T. H. Willcocks 
RMM # 12 
Dec. 1962 
p. 913 
Geometric magic squares 
Boris Kordemskii 
RMM:#13 
Feb. 1963 
p36 
I show these as Title, Author, JRM:volume #:issue #:date:pages(s)
Magic Designs 
Robert B. Ely III 
JRM:1:1:1968:317 
A Magic Square 
William J. Mannke 
JRM:1:3:1968:139 
Mannke's Order8 square 
Leigh Janes 
JRM:2:2:1969:96 
Construction of Odd Order Diabolic Magic Squares

J.A.H.Hunter 
JRM:2:3:1969:175177 
Sums of Third Order Antimagic Squares 
Charles W. Trigg 
JRM:2:4:1969:250254 
Triangles With Balanced Perimeters 
Charles W. Trigg 
JRM:3:4:1970:255256 
Fifth Order Concentric Magic Squares 
Charles W. Trigg 
JRM:4:1:1971:4244 
Domino & Superdomino Recreations II 
Wade E. Philpot 
JRM:4:1:1971:7987 
Schlegel Diagrams 
E. R. Ranucci 
JRM:4:2:1971:106113 
Doubly Magic Square with Remarkable Subsidiaries

Charles W. Trigg 
JRM:4:3:1971:171174 
Edge Magic and Edge Antimagic Tetrahedrons

Charles W. Trigg 
JRM:4:4:1971:253259 
Normal Magic Triangles of ordern 
Terrel Trotter 
JRM:5:1:1972:2832 
Edge Antimagic Tetrahedrons with Rotating Triads 
Charles W. Trigg 
JRM:5:1:1972:4042 
The Third Order Magic Cube Complete 
John R. Hendricks 
JRM:5:1:1972:4350 
The Pan3agonal Magic Cube 
John R. Hendricks 
JRM:5:1:1972:5152 
Perfectly Odd Squares 
Monk A. Ricci 
JRM:5:2:138142 
Latin Squares Under Restriction, and a Jumboization

N. T. Gridgeman 
JRM 5:3 1972:198202 
Magic Squares with Nonagonal & Decagonal Elements

Charles W. Trigg 
JRM:5:3:1972:203204 
The Pan3agonal Magic Cube of Order5 
John R. Hendricks 
JRM:5:3:1972:205206 
Magic Squares Embedded in a Latin Square 
N. T. Gridgeman 
JRM:5:4:1972:250 
Antimagic Squares With Sums in Arithmetic Progression 
Charles W. Trigg 
JRM:5:4:1972:278280 
GraecoLatin Cubes 
P.D. Warrington 
JRM:6:1:1973:4753 
The ArkinHoggartt Game & Solution to a Classical 
Arkin, J. & Hoggatt, Jr 
JRM:6:1:1973:120121 
Species of ThirdOrder Magic Squares & Cubes

John R. Hendricks 
JRM:6:3:1973:190192 
Magic Tesseracts & ndimensional Magic Hypercubes

John R. Hendricks 
JRM:6:3:1973:193201 
Magic Cubes of Odd Order 
John R. Hendricks 
JRM:6:4:1973:268272 
Trimagic Squares 
William H. Benson 
JRM:7:1:1974:813 
Perimeter Magic Polygons 
Terrel Trotter Jr. 
JRM:7:1:1974:1420 
Third Order Square Related to Magic Squares

Charles W. Trigg 
JRM:7:1:1974:2122 
Eight digits on a Cubes Vertices 
Charles W. Trigg 
JRM:7:1:1974:4955 
Exploded Myths 
Arkin, J. & Hoggatt, Jr 
JRM:7:1:1974:9093 
Pannagonals in Hypercubes 
John R. Hendrick 
JRM:7:2:1974:9596 
Not Every Magic Square is a Latin Square 
Joseph M. Moser 
JRM:7:2:1974:9799 
Some Properties of Third Order Magic Squares

Charles W. Trigg 
JRM:7:2:1974:100101 
9digit Determinants equal to Their 1st Rows

Charles W. Trigg 
JRM:7:2:1974:136139 
A Pandiagonal Magic Square of Order8 
John R. Hendrick 
JRM:7:3:1974:186 
Magic Square Time 
John R. Hendricks 
JRM:7:3:1974:187188 
Perfect Magic Cubes of Order Seven 
Bayard E. Wynne 
JRM:8:4:1975:285293 
Infinite Magic Squares 
Ronald J. Lanaster 
JRM:9:2:1976:8693 
58. Magic Squares 
Rudolf Ondrejka 
JRM:9:2:1976:128129 
Perfect Magic Icosapentacles 
Baynard E. Wynne 
JRM:9:2:1976:241248 
Pandiagonal Associative Magic Cubes… 
Ian P. Howard 
JRM:9:4:1976:276278 
Related Magic Squares with Prime Elements 
Gakuho Abe 
JRM:10:2:1977:9697 
Computer Constructed Magic Cubes 
Ronald J. Lancaster 
JRM:10:3:1977:202203 
Magic Talisman Squares 
GregFitzgibbon 
JRM:10:4:1977:279280 
Perimeter Antimagic Tetrahedrons 
Charles W. Trigg 
JRM:11:2:197879:105107 
Magic Triangular Regions of Orders 4 and 5

Usiskin & Stephanides 
JRM:11:3:197879:176179 
Magic Cubes of Prime Order 
K.W.H.Leeflang 
JRM:11:4:197879:241257 
The Perfect Magic Cube of Order4 
John R. Hendricks 
JRM:13:3:198081:204206 
A Family of Sixteenth Order Magic Squares .

Charles W. Trigg 
JRM:13:4:198081:269273 
The Pan3agonal Magic Cube of Order4 
John R. Hendricks 
JRM:13:4:198081:274281 
962. ConsecutivePrime Magic Squares 
Frank Rubin 
JRM:14:2:198182:152153 
A 32nd Order Magic Square With Tetrahedral Elements

Charles W. Trigg 
JRM:14:4:198182:246251 
Special Antimagic Triangular Arrays 
Charles W. Trigg 
JRM:14:4:198182:274278 
ConsecutivePrime Magic Squares 
Alan W. Johnson Jr. 
JRM:15:1:198283:1718 
A Bordered Prime Magic Square 
Alan W. Johnson Jr. 
JRM:15:2:198283:84 
The Construction of Doublyeven Magic Squares

Tien Tao Kuo 
JRM:15:2:198283:94104 
A Unique 9Digit Square Array 
Vittorio Fabbri 
JRM:15:3:198283:170171 
A Sixth Order Prime Magic Square 
Alan W. Johnson Jr. 
JRM:15:3:198283:199 
Magic Triangular Regions of Orders 5 and 6

Katagiri & Kobayashi 
JRM:15:3:198283:200208 
Irregular Perfect Magic Squares of Order 7

Gakuho Abe 
JRM:15:4:198283:249250 
Early Books on Magic Squares 
William L. Schaaf 
JRM:16:1:198384:16 
666 – Order 4 M. S. (Letter to the Editor)

Rudolf Ondrejka 
JRM:16:2:198384:121 
1219. The Magic Hexagon 
Charles W. Trigg 
JRM:16:4:19834:234 
Perfect Prime Squares 
Charles W. Trigg 
JRM:17:2:1985: 
9digit DigitRoot Magic & SemiMagic Squares

Charles W. Trigg 
JRM:17:2:1985:112118 
An Order4 Prime Magic Cube 
Alan W. Johnson, Jr. 
JRM:18:1:1986:57 
ThirdOrder
Gnomonmagic Squares 
Charles W. Trigg 
JRM:18:1:1986:2535 
Ten Magic Tesseracts of Order Three 
John R. Hendricks 
JRM:18:2:1986:125134 
A Magic Rooks Tour 
Stanley Rabinowitz 
JRM:18:3:1986:203204 
Thirdorder Gnomonmagic Squares with Distinct Prime Elements 
Charles W. Trigg 
JRM:19:1:1987:12 
Absolute
Difference Sums of ThirdOrder Toroids 
Charles W. Trigg 
JRM:19:1:1987:2023 
A Prime Magic Square for the Year 1987 
Alan W. Johnson Jr. 
JRM:19:1:1987:24 
Letter to the Editor Borders for 2ndorder square

John R. Hendricks 
JRM:19:1:1987:42 
Generating a Pandiagonal Magic Square of Order8

John R. Hendricks 
JRM:19:1:1987:5558 
Vestpocket Biblio. No. 12: Magic Squares & Cubes

William L. Schaaf 
JRM:19:2:1987:8186 
A Ninth Order Magic Cube 
John R. Hendricks 
JRM:19:2:1987:126131 
A Remarkable group of Gnomonantimagic Squares

Charles W. Trigg 
JRM 19:3:1987:164168 
Constructing Pandiagonal Magic Squares of Odd Order

John R. Hendricks 
JRM:19:3:1987:204208 
Magic Squares With Duplicate Entries 
Victor G. Feser 
JRM:19:3:1987:209212 
Algebraic Forms for Order Three Squares/Cubes

Alan W. Johnson Jr. 
JRM:19:3:1987:213218 
Absolute Differences In Thirdorder Triangular Arrays

Charles W. Trigg 
JRM 19:3:1987:219223` 
Commemorating the Constitution 
Alan W. Johnson Jr. 
JRM:19:4:1987:261263 
Creating Pan3agonal Magic Cubes of Odd Order

John R. Hendricks 
JRM:19:4:1987:280285 
A Magic Cube of Order 7 
John R. Hendricks 
JRM:20:1:1988:2325 
Some Ordinary Magic Cubes of Order 5 
John R. Hendricks 
JRM:20:1:1988:125134 
Related Magic Squires 
Alan W. Johnson Jr. 
JRM:20:1:1988:26 
Pandiagonal Magic Squares of Odd Order 
John R. Hendricks 
JRM:20:2:1988:8791 
Magic Cubes of Odd Order by Pocket Computer

John R. Hendricks 
JRM:20:2:1988:9296 
Problem 1549: An Odd Twist (solution by A. W. Johnson) 
John R. Hendricks 
JRM:20:2:1988:152153 
The Diagonal Rule for Magic Cubes of Odd Order

John R. Hendricks 
JRM:20:3:1988:192195 
More Pandiagonal Magic Squares 
John R. Hendricks 
JRM:20:3:1988:198201 
Perfect Order8 Cube (Letter to the Editor) 
Rudolf Ondrejka 
JRM:20:3:1988:207209 
A Consecutive Prime 3 x 3 Magic Square 
Harry L. Nelson 
JRM:20:3:1988:214216 
1574: "1987" Magic Squares (sol. by A.J, & F.K.)

Stanley Rabinowitz 
JRM:20:3:1988:235 
The Third Order Magic Tesseract 
John R. Hendricks 
JRM:20:4:1988:251256 
Another Magic Tesseract of Order3 
John R. Hendricks 
JRM:20:4:1988:275276 
Creating More Magic Tesseracts of Order3 
John R. Hendricks 
JRM:20:4:1988:279283 
Groups of Magic Tesseracts 
John R. Hendricks 
JRM:21:1:1989:1318 
More and More Magic Tesseracts 
John R. Hendricks 
JRM:21:1:1989:2628 
The Pan4agonal Magic Tesseract of Order4

John R. Hendricks 
JRM:21:1:1989:5660 
A Perfect 4_Dimensional Hypercube of Order7

Arkin Arney & Porter 
JRM:21:2:1989:8188 
Palindromes and Magic Squares 
Alan W. Johnson Jr. 
JRM:21:2:1989:97100 
Normal Magic Cubes of Order 4m+2 (Letter to Editor) 
Alan W. Johnson Jr. 
JRM:21:2:1989:101103 
Supermagic and Antimagic Graphs 
N.Hartsfield & G. Ringel 
JRM:21:2:1989:107115 
The Determinant of a Pandiagonal Magic Square is 0

John R. Hendricks 
JRM:21:3:1989:179181 
A 5Dimensional Magic Hypercube of Order5

John R. Hendricks 
JRM:21:4:1989: 245248 
The Magic Tesseracts of Order3 Complete 
John R. Hendricks 
JRM:22:1:1990: 1526 
A Square Magic Square 
Alan W. Johnson Jr. 
JRM:22:1:1990: 38 
The Secret of Franklin’s 8 x 8 Magic’ Square

Lalbhai D. Patel 
JRM:23:3:1991:175182 
Magic Squares Matrices Planes and Angles 
Frank E. Hruska 
JRM:23:3:1991:183189 
Minimum Prime Order6 Magic Squares 
Alan W. Johnson Jr. 
JRM:23:3:1991:190191 
Inlaid Odd Order Magic Squares 
John R. Hendricks 
JRM:24:1:1992:611 
A Note on Magic Tetrahedrons 
John R. Hendricks 
JRM:24:4:1992:244 
The Magic Hexagram 
John R. Hendricks 
25:1:1993:1012 
Frierson's Fuddle 
John R. Hendricks 
25:1:1993:177 
Prime Magic Squares for the Prime Year 1993

Alan W. Johnson Jr. 
JRM:25:2:1993:136137 
An Inlaid Magic Cube 
John R. Hendricks 
JRM:25:4:1993:286288 
Property of Some Pan3Agonal Magic Cubes of Odd Order

John R. Hendricks 
JRM:26:2:1994:96101 
Inlaid Pandiagonal Magic Squares 
John R. Hendricks 
JRM:27:2:1995:123124 
Inlaid Magic Squares 
John R. Hendricks 
JRM:27:3:1995:175178 
More Magic Squares 
Emanuel Emanouilidis 
JRM:27:3:1995:179180 
More Multiplication Magic Squares 
Emanuel Emanouilidis 
JRM:27:3:1995:181182 
Powers of Magic Squares 
Emanuel Emanouilidis 
JRM:29:3:1998:176177 
Palindromic Magic Squares 
Emanuel Emanouilidis 
JRM:29:3:1998:177 
Note on the Bimagic Square of Order3 
John R. Hendricks 
JRM:29:4:1998:265267 
Magic Squares of Order4 and Their Magic Square Loops

Robert S. Sery 
JRM:29:4:1998:265267 
A Partial Magic Tesseract of Order Two 
John R. Hendricks 
JRM:29:4:1998:290291 
Magic Reciprocals 
Jeffrey Haleen 
JRM:30:1:1999:7273 
Magic Rectangle 
E. W. Shineman, Jr. 
JRM:30:2:1999:111 
Magic Diamond for the New Millenium 
E. W. Shineman, Jr. 
JRM:30:2:1999:112 
From Inlaid Squares to Ornate Cube 
John R. Hendricks 
JRM:30:2:1999:125136 
Smarandache Magic Problem 2466 solution 
Charles Ashbacher 
JRM:30:4:1999:296299 
A Purely Pandiagonal 4x4 Square and the MyersBriggs Type
Table 
Peter D. Loly 
JRM:31:1:20022003:2931 
Problem 2584:
Prime Square 

JRM:31:1:20022003:71 
Concatenation on
Magic Squares 
Emanuel Emanouilidis 
JRM:31:2:20022003:110111 
Franklin's
"Other" 8Square 
Paul C. pasles 
JRM:31:3:20022003:161166 
Magic Lightning 
Edward W.
Shineman, Jr 
JRM:31:3:20022003:167 
Problem 2617:
Magic Cube of Primes 
Harvey D. Heinz 
JRM:31:4:20022003:298 
A Unified
Classification System for Magic Hypercubes 
H.Heinz &
D.Hendricks 
JRM:32:1:20032004:3036 
Problem 2584:
Solution 
Harvey Heinz 
JRM:32:1:20032004: 88 
Squareringed
Magic Squares 
Jeffrey Heleen 
JRM:32:2:20032004:144146 
kSets of n^{th}
Order Magic Squares 
D. Feil & A.
Shulman 
JRM:32:3:20032004: 181192 
The First (?) Magic Cube 
Harvey Heinz 
JRM:33:2:20042005:111115 
The First (?) Perfect Magic Cubes 
Harvey Heinz 
JRM:33:2:20042005:116119 
Bordered Magic Rectangle 
E.W.Shineman, Jr. 
JRM:33:3:20042005:180181 
In Memoriam: John Robert Hendricks:
Sept. 4, 1929  July 7, 2007 

JRM:34:1:20052006:8081 
The Order 5 General Bimagic Square 
Michael P. Cohen 
JRM:34:2:20052006:107111 
Everywhere Squares (of square #'s)
(Problems & Conjectures #2690 
Henry Ibstedt 
JRM:34:3:20052006:224226 
Magic Square Magnitudes (Problems &
Conjectures #2694) 
Kathleen Lewis 
JRM:34:3:20052006:228229 
A FourthOrder DigitallyReversible
Polylingual Bialphabic Alphamagic Square 
Lee B. Croft & Samuel Comi 
JRM:34:4:20052006:247257 
Hypercube Classes  An Update 
Harvey D. Heinz 
JRM:35:1:2006:510 
Magic Tesseract Classes 
H.D. Heinz & M. Nakamura 
JRM:35:1:2006:1114 
BehforoozEuler Knight Tour Magic
Square with U.S. Election Years 
Hossein Behforooz 
JRM:35:1:2006:2022 
BehforoozFranklin Magic Square with
U.S. Election Years 
Hossein Behforooz 
JRM:35:1:2006:3738 
Albrecht Durer and His Magic Square 
Owen O'Shea 
JRM 35:4 2006 285290 
Bimagic Squares of Order 13, 14, and 15 
Qinwu Chen & Xiufeng Liu 
JRM 35:4 2006 312317 
Weighted Magic Squares 
Hossein Behforooz 
JRM 36:4 2007 283286
(actually 2012) 
Behforooz Magic Squares Derived From
MagicLatinSudokuSquares 
Hossein Behforooz 
JRM 36:4 2007 287293
(actually 2012) 
Papers
on Magic Stars
In contrast to the voluminous literature for magic squares spanning 100's of
years, there has been very little published on magic stars. The main sources of
information I have been able to locate are:
H.E.Dudeney,
536 Puzzles & Curious Problems, Scribner's 1967. Pages 145147 and
347352.
Prof. Dr. F. Fitting, Panmagische Quadrate und
magische Sternvielecke, Panmagic squares and magic stars, 1939, 70
pages. Pages 52 to 70 are on magic stars including lots of diagrams.
Martin Gardner,
Mathematical Recreations column of Scientific American, Dec. 1965,
reprinted with addendum in Martin Gardner, Mathematical Carnival, Alfred A.
Knoff, 1975. Mostly on order 6, but mention made of total basic solutions for
orders 7 & 8 (also corrected number for order6).
Martin Gardner, Some New Results on Magic
Hexagrams,
College Mathematical Journal, 31, 4, Sept. 2000. pp 274280.
Max Bruno Lehmann, Der geometrische Aufbrau
Gleichsummiger Zahlenfiguren (The Geometric Construction of Magic Figures),
1875, xvi+384 pages.
This book is mostly about magic squares, but includes discussions and examples
of magic cubes and magic stars.
Reiter,
Harold B.,
A Magic Pentagram, Mathematics Teacher, Vol. 76, No. 3, Apr., 1983,
pp.174177.
Reiter, H. B. and
Ritchie, D.,
A Complete Solution to the Magic Hexagram, College Mathematical Journal,
20, 1989, pp 307316.
Schubert, Hermann, Mathematische Mussestunden
(Mathematical Pastimes)), 1963 reprint of 1900 work. Sections on various
subjects. pp172176 discuss magic stars. (This section was not in the original
or 1940 reprint).
Marián Trenkler
of Safarik University, Kosice, Slovakia published a paper on Magic Stars.
It is called "Magicke hviezdy" (Magic stars) and appeared in Obzory matematiky,
fyziky a informatiky, 51(1998), pages 17. (my copy is an English translation)
(Obzory = horizons (or line of sight) of mathematics, physics and informatics.
This material is the subject of my Trenkler Stars <trenkler.htm> page.
A modified version of this paper was subsequently published as
Magic Stars, The IIME Journal, vol. 11, No. 10, Spring 2004, pp549554.
Trigg,
Charles W.,
Multiplicative Magic Pentagram, School Science & Mathematics, ?, pp
673674
Perfect Magic
Icosapentacles 
Bayard E. Wynne

JRM:9:4:1976:241248 
Antimagic
Pentagrams with Consecutive Line Sums 
Charles W.
Trigg, 
JRM:10:3:1977:169173 
385. Do
Pentacles Exist 
Buckley,
Michael 
JRM:10:4:1977:288289 
A Magic
Asteriod 
Gakuho Abe

JRM:16:2:198384:113 
Magic Pentagram
Solutions Over GF(2) 
Harold Reiter

JRM:20:2:1988:99104 
Two New Magic
Asteroids 
Laurent Hodges

JRM:24:2:1992:8586 
The Magic
Hexagram 
John R.
Hendricks 
JRM:25:1:1993:1012 
Letter to the
Editor (Magic Asteroids) 
Alan W. Johnson
Jr. 
JRM:26:2:1994:9091 
Almost Magic

Charles W.
Trigg 
JRM:29:1:1998:811 
As mentioned at the top of the page, the above lists represent only books or
articles that are in my library or that I have actually seen (except for the pre
1900 books mentioned at the start). For this reason, this bibliography should
not be considered complete.
DVD's
Heinz, Harvey D., Magic Hypercube Omnibus, HDH
Publishing, 2011, 9780968798515. Limited production for free
distribution. See Omnibus
here.
