The Zen of Magic Squares, Circles, and Stars

An Exhibition of Surprising Structures across Dimensions

Author: Clifford A. Pickover

Publisher: Princeton University Press

ISBN: 1400841518

Category: Mathematics

Page: 432

View: 563

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Humanity's love affair with mathematics and mysticism reached a critical juncture, legend has it, on the back of a turtle in ancient China. As Clifford Pickover briefly recounts in this enthralling book, the most comprehensive in decades on magic squares, Emperor Yu was supposedly strolling along the Yellow River one day around 2200 B.C. when he spotted the creature: its shell had a series of dots within squares. To Yu's amazement, each row of squares contained fifteen dots, as did the columns and diagonals. When he added any two cells opposite along a line through the center square, like 2 and 8, he always arrived at 10. The turtle, unwitting inspirer of the ''Yu'' square, went on to a life of courtly comfort and fame. Pickover explains why Chinese emperors, Babylonian astrologer-priests, prehistoric cave people in France, and ancient Mayans of the Yucatan were convinced that magic squares--arrays filled with numbers or letters in certain arrangements--held the secret of the universe. Since the dawn of civilization, he writes, humans have invoked such patterns to ward off evil and bring good fortune. Yet who would have guessed that in the twenty-first century, mathematicians would be studying magic squares so immense and in so many dimensions that the objects defy ordinary human contemplation and visualization? Readers are treated to a colorful history of magic squares and similar structures, their construction, and classification along with a remarkable variety of newly discovered objects ranging from ornate inlaid magic cubes to hypercubes. Illustrated examples occur throughout, with some patterns from the author's own experiments. The tesseracts, circles, spheres, and stars that he presents perfectly convey the age-old devotion of the math-minded to this Zenlike quest. Number lovers, puzzle aficionados, and math enthusiasts will treasure this rich and lively encyclopedia of one of the few areas of mathematics where the contributions of even nonspecialists count.

Before Sudoku

The World of Magic Squares

Author: Seymour S. Block,Santiago Alves Tavares

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Games

Page: 239

View: 7461

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Sudoku has become a vastly popular and even addictive game. But fans may not know that Sudoku is a recent offshoot of the venerable Magic Square, which dates back over 4,000 years to ancient China, where it was literally considered magical. Indeed, Magic Squares have fascinated centuries of mystics, astrologers, and some of the world's most brilliant thinkers, including Ben Franklin. In Sudoku and Magic Squares, Seymour Block and Santiago Tavares offer a crystal clear and engagingtour tour of Magic Squares, tracing their footsteps through through ancient and medieval history and illuminating their uses in art and design, statistics and electronics. The book provides a delightful account of a mind-boggling variety of magical squares, ranging from simple 3 x 3 and squares, to magic cubes, magic circles, magic pyramids, and even "the Beastly Magical Square," whose magic sum is 666. Of course, the authors also cover Sudoku, describing how the game became a world-wide phenomenon and revealing various strategies for solving the puzzles. And along the way, the book offers readers many fascinating facts - for instance, Sudoku was invented in 1979 by an American architect living in Indianapolis and was originally called Number Place. Oddly enough, though the puzzle is known around the world by its Japanese name (which means "single numbers"), many Japanese still call it Number Place. We also learn that in a 4 x 4 magic square, there are 880 different solutions that will yield the magic sum of 34 - a surprisingly large number until you remember that there are over 2.6 trillion possible combinations. Filled with lots of original puzzles for gamers to solve, Sudoku and Magic Squares is an entertaining book that will delight anyone who loves a challenge, including all fans of Sudoku.

Legacy of the Luoshu

The 4,000 Year Search for the Meaning of the Magic Square of Order Three

Author: Frank Swetz

Publisher: CRC Press

ISBN: 1439865329

Category: Mathematics

Page: 228

View: 7542

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A symbol of the Divine, a good luck charm, a cosmogram of the world order, a template for fengshui —through the ages, the luoshu, or magic squre of order three, has fascinated people of many different cultures. In this riveting account of cultural detective work, renowned mathematics educator, Frank J. Swetz relates how he uncovered the previously hidden history of the luoshu, from its Chinese origins, shrouded in legend, through its eventual association with Chinese fortunetelling, Daoism, and fengshui, to its incorporation into Islamic astrology and alchemy and its migration into Kabbalistic lore and other occult traditions of the West.

Magic squares

Author: Paul Calter

Publisher: N.A

ISBN: N.A

Category: Computer programming

Page: 143

View: 8799

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Before Sudoku

The World of Magic Squares

Author: Seymour S. Block,Santiago Alves Tavares

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Games

Page: 239

View: 8774

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Sudoku has become a vastly popular and even addictive game. But fans may not know that Sudoku is a recent offshoot of the venerable Magic Square, which dates back over 4,000 years to ancient China, where it was literally considered magical. Indeed, Magic Squares have fascinated centuries of mystics, astrologers, and some of the world's most brilliant thinkers, including Ben Franklin. In Sudoku and Magic Squares, Seymour Block and Santiago Tavares offer a crystal clear and engagingtour tour of Magic Squares, tracing their footsteps through through ancient and medieval history and illuminating their uses in art and design, statistics and electronics. The book provides a delightful account of a mind-boggling variety of magical squares, ranging from simple 3 x 3 and squares, to magic cubes, magic circles, magic pyramids, and even "the Beastly Magical Square," whose magic sum is 666. Of course, the authors also cover Sudoku, describing how the game became a world-wide phenomenon and revealing various strategies for solving the puzzles. And along the way, the book offers readers many fascinating facts - for instance, Sudoku was invented in 1979 by an American architect living in Indianapolis and was originally called Number Place. Oddly enough, though the puzzle is known around the world by its Japanese name (which means "single numbers"), many Japanese still call it Number Place. We also learn that in a 4 x 4 magic square, there are 880 different solutions that will yield the magic sum of 34 - a surprisingly large number until you remember that there are over 2.6 trillion possible combinations. Filled with lots of original puzzles for gamers to solve, Sudoku and Magic Squares is an entertaining book that will delight anyone who loves a challenge, including all fans of Sudoku.

Choice

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Best books

Page: N.A

View: 9840

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Mathematical Magic

Author: William Simon

Publisher: Courier Corporation

ISBN: 9780486275932

Category: Mathematics

Page: 187

View: 9273

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Stimulating treasury of entertaining tricks, stunts, and magical effects based on such mathematical principles and ideas as magic squares, the Fibonacci Series, Moebius strips, cycloids, topology, and more. Only simple props required: from playing cards and matches to coins. No magic or mathematical skills needed.

The Loom of God

Tapestries of Mathematics and Mysticism

Author: Clifford A. Pickover

Publisher: Sterling Publishing Company, Inc.

ISBN: 9781402764004

Category: Mathematics

Page: 287

View: 8472

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Previous ed. published in 1997 under the title: The loom of God: mathematical tapestries at the edge of time, by Plenum Press.

Algorithmic Puzzles

Author: Anany Levitin,Maria Levitin

Publisher: OUP USA

ISBN: 0199740445

Category: Computers

Page: 257

View: 1562

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Algorithmic puzzles are puzzles involving well-defined procedures for solving problems. This book will provide an enjoyable and accessible introduction to algorithmic puzzles that will develop the reader's algorithmic thinking. The first part of this book is a tutorial on algorithm design strategies and analysis techniques. Algorithm design strategies — exhaustive search, backtracking, divide-and-conquer and a few others — are general approaches to designing step-by-step instructions for solving problems. Analysis techniques are methods for investigating such procedures to answer questions about the ultimate result of the procedure or how many steps are executed before the procedure stops. The discussion is an elementary level, with puzzle examples, and requires neither programming nor mathematics beyond a secondary school level. Thus, the tutorial provides a gentle and entertaining introduction to main ideas in high-level algorithmic problem solving. The second and main part of the book contains 150 puzzles, from centuries-old classics to newcomers often asked during job interviews at computing, engineering, and financial companies. The puzzles are divided into three groups by their difficulty levels. The first fifty puzzles in the Easier Puzzles section require only middle school mathematics. The sixty puzzle of average difficulty and forty harder puzzles require just high school mathematics plus a few topics such as binary numbers and simple recurrences, which are reviewed in the tutorial. All the puzzles are provided with hints, detailed solutions, and brief comments. The comments deal with the puzzle origins and design or analysis techniques used in the solution. The book should be of interest to puzzle lovers, students and teachers of algorithm courses, and persons expecting to be given puzzles during job interviews.

The Pythagorean Sourcebook and Library

An Anthology of Ancient Writings Which Relate to Pythagoras and Pythagorean Philosophy

Author: David R. Fideler

Publisher: Red Wheel/Weiser

ISBN: 1609253949

Category: Philosophy

Page: 362

View: 3190

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Pythagoras (fl. 500 B.C.), the first man to call himself a philosopher or lover of wisdom, was both a brilliant mathematician and spiritual teacher. This anthology, the largest collection of Pythagorean writings ever to appear in the English language, contains the four ancient biographies of Pythagoras and over 25 Pythagorean and Neopythagorean writings from the Classical and Hellenistic periods. The Pythagorean ethical and political tractates are especially interesting for they are based on the premise that the universal principles of Harmony, Proportion, and Justice govern the physical cosmos, and these writings show how individuals and societies alike attain their peak of excellence when informed by these same principles. Indexed, illustrated, with appendices and an extensive bibliography, this acclaimed anthology also contains a foreword by Joscelyn Godwin and an introductory essay by the editor, David Fideler.

The Art of Game Design

A Book of Lenses, Second Edition

Author: Jesse Schell

Publisher: CRC Press

ISBN: 1498759564

Category: Computers

Page: 600

View: 8433

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Good game design happens when you view your game from as many perspectives as possible. Written by one of the world's top game designers, The Art of Game Design presents 100+ sets of questions, or different lenses, for viewing a game’s design, encompassing diverse fields such as psychology, architecture, music, visual design, film, software engineering, theme park design, mathematics, puzzle design, and anthropology. This Second Edition of a Game Developer Front Line Award winner: Describes the deepest and most fundamental principles of game design Demonstrates how tactics used in board, card, and athletic games also work in top-quality video games Contains valuable insight from Jesse Schell, the former chair of the International Game Developers Association and award-winning designer of Disney online games The Art of Game Design, Second Edition gives readers useful perspectives on how to make better game designs faster. It provides practical instruction on creating world-class games that will be played again and again.

Mathematics Today

Bulletin of the Institute of Mathematics and Its Applications

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 5820

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I Am a Strange Loop

Author: Douglas R. Hofstadter

Publisher: Basic Books

ISBN: 0465030785

Category: Philosophy

Page: 412

View: 3480

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An original, endlessly thought-provoking, and controversial look at the nature of consciousness and identity argues that the key to understanding selves and consciousness is the "strange loop," a special kind of abstract feedback loop inhabiting our brains.