Magic Squares - References
The following list includes a number of books, in order of author, that
contain references to Magic Squares. The list is not intended to be
exhaustive, but it is representative of the range of both mathematical
and magical literature that is available on this fascinating subject:
- Allerton, Bert (1958) Close Up Magician
- Anderson, Harry & Racherbaumer, Jon (2008) Magic Squared.
- A treatise on the venerable Magic Square as a performance piece, showcasing Harry Anderson's unique presentations. History, essays and a bibliography by Jon Racherbaumer add gravitas to this important publication. Limited to 200 numbered copies signed by Harry Anderson in this first printing.
- Andrews, W. S. (1960) Magic Squares And Cubes.
New York, New York: Dover (and London: Constable & Company Limited)
- This is probably the definitive work on Magic Squares. It shows how to construct them, the
detailed mathematics behind them, and all of the many variations that exist. It is also a
highly "technical" book, and of more interest to the serious mathematician than the average
- Annemann, Theo. (1931) The Book Without A Name
- This book contains some good presentation tips.
- Anon. Internet
- There are many "pages" on the Internet about Magic Squares.
- Anon. The Complete Home Entertainer. London: Odhams Press
- This is quite an old book that I found on my local market. It contains a number of chapters
on magic, and one on word games, one of which is an early Latin Word Square.
- Anon. (c. 1890) National Encyclopaedia.
- Volume IX of this Victorian encyclopaedia contains a small entry
on Magic Squares, with an unusual example being shown of an 11 x 11
Magic Square that sums to a "Magic Total" of 24,156.
- Barlow, F. (1951) Mental Prodigies. London:
- This book is primarily concerned with a study of mental prodigies (e.g. lightning
calculators). However, a few chapters are devoted to the explanation of some of the methods
used by such people, including one brief chapter on Magic Squares.
- Becker, L. (1986) The Larry Becker Lecture. London: Lewis
- This video is a lecture on mentalism, and is only available to bona fide magicians. It
contains a number of unexplained items from Larry’s show, including his famous "Russian
Roulette" routine, a number of "lecture" items which are demonstrated and fully explained, and
finally a number of marketed items, which are also demonstrated and explained. One of the
"lecture" items, called "Déjà Vu", is of particular interest.
- Benson, W. H. & Jacoby, O. (1976) New Recreations With Magic
Squares. New York, New York: Dover (and London: Constable & Company
- This is a book that covers all orders of Magic Squares but is also oriented towards a
mathematical analysis of Magic Squares rather than any magical presentations.
- Benson, W. H. & Jacoby, O. (1981) Magic Cubes. New York, New York:
Dover (and London: Constable & Company Limited)
- This book is entirely devoted to Magic Cubes, and follows on from many of the techniques
published in their earlier book, "New Recreations With Magic Squares" (see above).
- Blaisdell, F. (1978) Magical Fun With Magic Squares. Oakland,
California: Magic Limited
- This book contains a number of innovative presentations of Magic Squares, and is only
available to bona fide magicians.
- Brandreth, G. (1984) Solo Games. London: Pan Books
- This book contains a number of puzzles and games for one person. One of the puzzles
involves creating a 6 x 6 Magic Square using 18 dominoes from a double-six set.
- Britland, D. (2002) The Mind & Magic of David Berglas. Burbank, California: Hahne Publications
- This is the long-awaited book that is more like a biography of David Berglas and his amazing magic than a typical magic book. It sold out of its 1,000 copies almost immediately. The book contains two excellent Magic Square routines.
- Carlisle, S. (1979) Dynamic Mentalism. Bideford,
Devon: The Supreme Magic Company
- This book, by one of the most well-known magicians in the field of mentalism, contains a
lecture demonstration based upon Magic Squares, as well as a chapter on memory. It is only
available to bona fide magicians.
- Cavendish, R. (1967) The Black Arts.
New York: The Berkley Publishing Group
- Although this book is about "black magic", it does describe a few Magic Squares.
- Clarke, J. (1969) Number Relationships 3 - The Magic Square.
Leeds: E. J. Arnold & Son Limited
- This book is one of a series of "programmed learning" books for schoolchildren of at least
ten years, and uses a 3 x 3 Magic Square to demonstrate the relationships between different
- Corinda, A. (1968) 13 Steps To Mentalism. New York, New York:
- This is another classic book on mentalism, only available to bona fide magicians, which has
one lesson (Step 3, largely written by David Berglas) devoted to 5 x 5 Magic Squares, mnemonics
and mental systems. For further information, the reader is referred to "Mental Prodigies" by
- Crane, Loch David (2009) Performer’s Guide To Magic Squares.
- Annemann’s Magic Squares improved, triple checked, and printed! Just copy on your tablet and walk out to present it; or keep open on your table, reading numbers as you pretend to calculate cells. Requires no math skills for a stunning display with a comedy finish.
- Dalal, Sam (Unknown) Patterns of Perfection: The Inner Secret Of The Magic Square.
- This is a soft cover, A-4 28 pages book illustrated with figure charts. The Magic Square is not as popular as other magic tricks among the magicians around the world. Perhaps the reason is because the systems available involve memory work, and complex mathematical calculations.
However, a Magic Square is something most people know and they are aware of the effort required to construct one. Therefore, when the magician successfully forms a magic square with any number given, people know that the feat has to be appreciated. A magic square has many interesting features, and can be customised to a spectator's date of birth, as a lucky amulet.
A Magic Square is the cheapest feature effect that one can perform, and a three-minute routine can be stretched as long as the performer wishes.
This book 'Patterns of Perfection' is a totally new "patterned" approach to the Magic Square. Anyone with average intelligence can master it in less than an hour by just reading this book, grasping the contents and with a few trials for practice. There are no mnemonics or memory system. No complicated mental arithmetic. You just need to know the secrets given in this book. Anybody can learn the secrets from this book and amuse the viewers with his amazing skill.
- Dexter, W. (1974) Feature Magic For Mentalists.
Bideford, Devon: The Supreme Magic Company
- This is a very useful book on mentalism, only available to bona fide magicians, with one
chapter which is devoted to mathematical magic. One part of this chapter is devoted to Magic
- Dudeney, Henry. (1958) Amusements In Mathematics. Dover
- Dudeney, Henry. (1932) Puzzles And Curious Problems. T. Nelson & Sons
- Dudeney, Henry. The Canterbury Puzzles.
- Dyment, Doug. Mindsights.
- Included in this book is the ability to quickly produce a magic square for an audience-selected number, which is always impressive, and because of this has been featured, both as a close-up performance item and as a popular "opener", by numerous entertainers. The problem with many such routines, however, is that (1) the squares are not as "magical" as they might be, (2) the mathematics are a struggle, (3) the construction method does not work well for large numbers, and/or (4) the technique does not bear repetition, as the resulting squares are too similar. The new approach explained here yields squares that add to the chosen number in more than two dozen different and interesting ways, can be produced in less than ten seconds with no more than a single subtraction, works with numbers of almost any magnitude, and can be repeated nearly three dozen times for the same audience (even the same target number) with no apparent duplication, making it suitable for walk-around, trade shows, etc.
- Encyclopaedia Britannica Inc. (1993) Encyclopaedia
Britannica ®. Chicago, Illinois: Encyclopaedia Britannica Inc.
- This well-known encyclopaedia, which contains entries on thousands of subjects, has a short
entry on Magic Squares (in Volume 7 of the 15th Edition of the Micropaedia Ready-Reference).
- Falkener, E. (1961) Games Ancient And Oriental And
How To Play Them. New York, New York: Dover
- This book, originally published in 1892, contains details of ancient Egyptian games (e.g.
tau, senat, ham), chess, draughts, backgammon, and also Magic Squares and Knight’s Tours.
- Farrar, Mark S. (2003) How To Create A Birthday Magic Square. Mark S. Farrar
- This short eBook describes how to create a 4 x 4 Magic Square, where the top row is somebody's birth date (or other specified date).
- Farrar, Mark S. (1996) Magic Squares. Mark S. Farrar
- This book covers many different aspects of Magic Squares, including their history, various methods of creating them, detailed analyses, and their use in magic effects.
- Fisher, John (1973) The Magic Of Lewis Carroll. Bramhall House
- This book is about recreational mathematics.
- Fults, John Lee (1974) Magic Squares. Open Court
- Fulves, K. (1983) Adrian Smith's Instant Magic Square. Fulves
- Fulves, K. (1983) Self-Working Number Magic. New York, New York:
Dover (and London: Constable & Company Limited)
- This is one of the excellent "Self-Working" series by this renowned author. This particular
one contains a number of effects using the Magic Square principle.
- Gardner, M. (1956) Mathematics Magic And Mystery.
New York, New York: Dover (and London: Constable & Company Limited)
- This is a similar book to "Mathematical Magic Show" (see below). The book is full of
tricks, games and puzzles, all of which have a mathematical nature.
- Gardner, M. (1965) Mathematical Puzzles And Diversions.
Harmondsworth, Middlesex: Pelican Books
- This book is entirely full of puzzles of a mathematical nature, but there is one chapter
devoted to magic with a matrix.
- Gardner, M. (1966) More Mathematical Puzzles And Diversions.
Harmondsworth, Middlesex: Pelican Books
- This is another book in the "leisure mathematics" series, which is full of tricks, games and
puzzles, all of which have a mathematical nature. Chapter 12 is devoted to Magic Squares.
- Gardner, M. (1978) Mathematical Carnival. Harmondsworth, Middlesex:
- This is one of many books by this prolific author, whose interests include both magic and
mathematics. There is one chapter devoted to Magic Stars and Magic Polyhedrons.
- Gardner, M. (1985) Mathematical Magic Show. London: Penguin
- This book is entirely devoted to mathematical magic, as its title suggests, with various
effects using the Magic Square principle.
- Gardner, M. (1985) The Magic Numbers Of Dr. Matrix. Buffalo, New
York: Prometheus Books
- This is a book which is primarily concerned with numerology and number theory, which
mentions Magic Squares in several places.
- Gardner, M. (1961) The 2nd Scientific American Book Of Mathematical Puzzles And Diversions. Simon & Schuster
- The chapter on Magic Squares has excellent background material.
- Gardner, M. (1988) Time Travel And Other Mathematical Bewilderments. New York, New York: W H Freeman & Company
- This is another book by this prolific author on various aspects of magic, including Magic
- Heath, R. V. (1953) Mathemagic. New York, New
York: Dover (and London: Constable & Company Limited)
- First written in 1933, this is a classic of mathematical magic. As far as Magic Squares are
concerned, there is an entire chapter devoted to the creation and transposition of Magic
Squares, and also other related formations (e.g. Magic Triangles).
- Hilliard, J. N. (1994) Greater Magic. Kaufman & Greenberg
- This is one of the classic magic books, recently republished and only available to bona fide
magicians, covering practically every subject possible. One chapter is devoted to the creation
and presentation of Magic Squares.
- I.B.M. The Linking Ring. St. Louis, Missouri:
International Brotherhood Of Magicians
- The Linking Ring is the official magazine of the International Brotherhood Of Magicians, and
is therefore only available to accredited members. There have undoubtedly been many references
to Magic Squares over the years in this magazine, but the ones mentioned here are of particular
- The September 1954 edition contains an article by A A A Almon called "Magic Square for 1955 and Numerology".
- The September 1954 edition contains an article by Rusduck called "M-A-G-I-C-U-B-E".
- The December 1956 edition contains an article by S Jackson Coleman called "Maneuvers with Mathemagitrix".
- The May 1962 edition contains an article by John Braun called "Benjamin Franklin's Ingenious Magic Square.
- The August 1963 edition contains an article by Clyde F Cairy called "Magic Squares in Iran".
- The October 1985 edition contains details of a Magic Square application by Max Maven.
- The July 1995 edition contains a routine by Gary Ward that uses the Max Maven application.
- Johnson, R. (1980) The Voice Of Experience, Vol. 1, Side 2. Martin Breese, England
- Johnson, R. (1995) Unique. Oadby, Leicestershire:
- This is one of Roy Johnson’s set of lecture notes, only available to bona fide magicians,
which contains one item, called "To Hell And Back", that will be of interest to mentalists.
- Kane, P. (1989) Kane At Table. Peter Kane
- This is a set of lecture notes, only available to bona fide magicians, in which one of the
explained effects has a Magic Square theme.
- Kaprekar, D. R. (1974) The Copernicus Magic Square. Indian Journal Of History Of Science, Vol. 9, No. 1
- Kaye, Marvin (1975) The Handbook Of Mental Magic. Stein and Day
- Chapter 14 is entitled "Super Memory and Rapid Calculation", which includes both mnemonics
and a 5 x 5 Magic Square.
- Kordemsky, B. (1975) The Moscow Puzzles. Harmondsworth, Middlesex:
- This is a book full of mathematical puzzles, but there is a small section (problems 331 -
339) on Magic Squares. It covers, briefly, the history of them, how to create them, and a few
other interesting facts and problems.
- Kraitchik, M. (1943) Mathematical Recreations. London: Allen &
- This is a book on general recreational mathematics, but it does include a section on Magic
Squares. The book is quite detailed in nature, but is oriented towards a mathematical analysis
of its contents rather than any magical presentations.
- Lorayne, H. (1977) The Magic Book. London:
W. H. Allen
- This is a magic book written for non-magicians as a beginners’ book. One of the chapters
covers number magic, with a method of creating an "instant" Magic Square included.
- MacGregor-Mathers, S.L. (1976) The Book of the Sacred Magic of Abra-Melin the Mage. New York, New York: Dover Publications
- Medieval manuscript of ceremonial magic. Basic document in Aleister Crowley, Golden Dawn groups.
- Meyer, O. (1961) The Amazing Magic Square & Master
Memory Demonstration. Cheyenne, Wyoming: Orville Meyer
- This relatively short booklet contains one of the best routines to be based on Magic
Squares, although it may be hard to find nowadays, especially as it is only available to bona
- Moran, J. (1982) The Wonders Of Magic Squares. New York, New York:
Random House, Inc.
- This book, written by a self-confessed "amateur recreational mathematician", is full of many
different ways of creating Magic Squares.
- Murray, B. (1989) Paul Daniels’ Adult Magic. London: Michael O’Mara Books Limited
- This book is relatively well-known, and contains a variety of reasonably simple magic
effects. There are a few pages on the subject of Magic Squares.
- Ollerenshaw, Kathleen & Bree, David (1998) Most-perfect Pandiagonal Magic Squares: Their Construction and Enumeration. Minneapolis
The Institute of Mathematics and its Applications
- This book gives a method of construction and enumeration of all pandiagonal magic squares of a class known as 'most-perfect'. Pandiagonal magic squares have the integers in all rows, all columns and all diagonals adding to the same sum. Characteristically, all integers come in complementary pairs along the diagonals and the integers in any 2 x 2 block of four add to the same sum. This is the first time, in thousands of years of mathematical experience that a method of construction has been found for a whole class. Formulas are given for the enumeration of all most-perfect squares, however large.
- Pickover, Clifford (2003) The Zen of Magic Squares, Circles, and Stars. Princeton University Press
- Subtitled "An Exhibition of Surprising Structures across Dimensions", this is a contemporary and comprehensive book on current magic square topics and ideas, by an accomplished (and popular) mathematical author. 405 pages.
- Pickover, Clifford (2003) Wonders Of Numbers. U.S.A.:
Oxford University Press Inc.
- This book on various aspects of mathematics includes several Magic Squares.
- Raven, A. (1974) The Necromantic Grimoire Of
Augustus Rupp. Waldwick, New Jersey: Bob Lynn
- This book, which is a limited edition only available to bona fide magicians, "reproduces" a
book of magic spells, symbols and other information, but includes two Word Squares.
- Riding, J. (1994) Close Up Club. St. Annes, Lancashire: Joe
- This is a twelve-part course in close-up magic, only available to bona fide magicians.
Joe’s new effect, "Computer Error", which is a routine for presenting a Magic Square, is
included in the final lesson, but will also be published separately.
- Rightmire, Richard (1972) The Master Mentalist. Micky Hades Enterprises
- Roth, David M. (1970) The Magic Square. Magic Limited
- Simon, W. (1965) Mathematical Magic. London:
Allen & Unwin
- This book is entirely devoted to mathematical magic, as its title suggests. However, there
is one chapter on the subject of Magic Squares, including both how to create them and some ideas
for using and presenting them.
- Simpson, D.C. (2001) Solving Magic Squares. United Kingdom:
1st Books Library
- This book provides generic solutions for creating various types of Magic Squares.
- Singer, J. (1994) Microsoft Encarta 1996 ®. Microsoft
- This is an encyclopaedia, stored on a CD-ROM, for use on a multimedia personal computer,
which contains one entry on Magic Squares.
- Smith, A. (1992) Cards On Call. Rotherham: Al Smith
- This book is not particularly related to mental magic or Magic Squares, as its title
suggests, and it is only available to bona fide magicians. However, there is one effect,
"Numorator", which is an interesting addition to a performer's repertoire of Magic Square
- Smith, A. (2002) Round The Square. Abacus Press Yorkshire
- Available to magicians, this book teaches a variety of fairly standard methods for constructing magic squares of orders four through seven, along with some other matrix-related topics. 73 pages.
- Smith, H. Adrian (1933) Master Mysteries Of 1933.
- Snader, C.M. (1985) Mind Square. Mexico: Exclusive Magical Publications
- This book contains a method for creating a 4 x 4 Magic Square, including an "instant"
- Starkes, Bob Seven Magic Squares In One. Ledgerdemain
- Steele, Rufus (1952) The Last Work On Cards.
- Swetz, Frank (2001) Legacy Of The Luoshu. Chicago
Open Court Publishing Company
- This book is the first study of the magic square, or Luoshu, as a cultural artifact and spiritual symbol as well as mathematical expression. A magic square is an arrangement of numbers (with no number duplicated) where the rows, columns, and two main diagonals add up to the same number, the magic constant. Originally devised by the ancient Chinese, who viewed it as a symbol of metaphysical and spiritual harmony, the magic square was brought to the West by Arab traders. In Legacy of the Luoshu, the author examines how various people in diverse societies have been drawn to the impressive regularity of number patterns and how cultural beliefs can be expressed through the symbolism of numbers. This is an entertaining read for anyone interested in popular mathematics and finding similarities of beliefs and symbols across cultures.
- Tahan, M. (1994) The Man Who Counted. Edinburgh:
- This is a book that explores various aspects of mathematics via a
series of stories told about a mathematician called Beremiz Samir.
There are a couple of pages that describe, simply, Magic Squares.
- Thompson Jr., J. G. (1975) The Miracle Makers. Magic Limited
- This contains an interesting idea for a 5 x 5 Magic Square.
- Tucker, S. (1992) Card Bored?. Great Malvern, Worcestershire:
- This is a book of various close-up routines, mainly using playing
cards, which is only available to bona fide magicians. However, there
are also three routines ("The Square Comes Full Circle", "The Almost
Magic Square" and "Sweet Sixteen") that involve Magic Squares.
- Van Delft, P. & Boterman, J. (1978) Creative Puzzles
Of The World. London: Cassell Ltd.
- This book contains an excellent collection of puzzles from all over
the world, as its title implies. There is a small but interesting and
varied section on Magic Squares.
- Young, Morris N. Hobby Magic.
- Wells, D. (1986) The Penguin Dictionary Of Curious
And Interesting Numbers. London: Penguin Books
- Whilst not a magic book, this does contain some fascinating
mathematical information, some of which can be used to enhance the
presentation of a Magic Square demonstration.
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Created: Tuesday 30th December, 1997
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