The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures across Dimensions

Princeton University Press
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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.

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About the author

Clifford Pickover is the author of over twenty books on a broad range of topics in science and art, a columnist for Odyssey, and an inventor. His books include Surfing Through Hyperspace: Understanding Higher Universes in Six Easy Lessons, Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning, and The Loom of God: Mathematical Tapestries at the Edge of Time.
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Additional Information

Publisher
Princeton University Press
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Published on
Nov 28, 2011
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Pages
432
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ISBN
9781400841516
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Language
English
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Genres
Mathematics / History & Philosophy
Mathematics / Recreations & Games
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Content Protection
This content is DRM protected.
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Read Aloud
Available on Android devices
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Eligible for Family Library

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Clifford A. Pickover
Do a little armchair time-travel, rub elbows with a four-dimensional intelligent life form, or stretch your mind to the furthest corner of an uncharted universe. With this astonishing guidebook, Surfing Through Hyperspace, you need not be a mathematician or an astrophysicist to explore the all-but-unfathomable concepts of hyperspace and higher-dimensional geometry. No subject in mathematics has intrigued both children and adults as much as the idea of a fourth dimension. Philosophers and parapsychologists have meditated on this mysterious space that no one can point to but may be all around us. Yet this extra dimension has a very real, practical value to mathematicians and physicists who use it every day in their calculations. In the tradition of Flatland, and with an infectious enthusiasm, Clifford Pickover tackles the problems inherent in our 3-D brains trying to visualize a 4-D world, muses on the religious implications of the existence of higher-dimensional consciousness, and urges all curious readers to venture into "the unexplored territory lying beyond the prison of the obvious." Pickover alternates sections that explain the science of hyperspace with sections that dramatize mind-expanding concepts through a fictional dialogue between two futuristic FBI agents who dabble in the fourth dimension as a matter of national security. This highly accessible and entertaining approach turns an intimidating subject into a scientific game open to all dreamers. Surfing Through Hyperspace concludes with a number of puzzles, computer experiments and formulas for further exploration, inviting readers to extend their minds across this inexhaustibly intriguing scientific terrain.
Matt Parker
Jordan Ellenberg
The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands

The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it.

Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer?

How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God.

Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.
Clifford A. Pickover
Från Pytagoras till den 57:e dimensionen här kommer 250 milstolpar i matematikens historia.

Matematiken är evig. Den fanns långt före oss människor och kommer att leva långt efter att vi försvinner som existenser i universum. Följ med på en svindlande resa genom matematikens historia här på vår jord.

På 528 sidor gås 250 historiska matematiska milstolpar igenom allt illustrerat med fotografier. Bokens författare tar ett brett grepp om matematikens historia och går bortom de matematiska principer och teorier som formulerats av oss människor. Allt presenteras i kronologisk ordning och bokens första avsnitt tar avstamp i en myra som fanns redan för 150 miljoner år sedan Cataglyphis fortis.

Boken riktar sig till en bred publik såväl matematiker som lekmän intresserade av ämnet och ger en översiktlig och inspirerande introduktion till viktiga matematiska idéer och matematiska tänkare. Varje avsnitt tar några minuter att läsa och förutom de självklara kandidaterna som Pytagoras sats, Einsteins E=mc2, Nash-jämvikt och Boolesk algebra, så får man här även läsa om uppfinnaren av miniräknaren, Rubiks kub och tillkomsten av siffran 0.

Funderar du på om det går att vända en sfär ut och in eller undrar du vad en evighet är? Frågar du dig hur det gick till när vi övergav romerska siffror eller vem den första kända matematikern var? Om någon av dessa frågor väcker din nyfikenhet så kommer du att hitta mycket spännande att läsa i denna bok.

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