The Zen of Magic Squares, Circles, and Stars
An Exhibition of Surprising Structures across Dimensions
Seiten
2002
Princeton University Press (Verlag)
978-0-691-07041-4 (ISBN)
Princeton University Press (Verlag)
978-0-691-07041-4 (ISBN)
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Provides an explanation of 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.
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 book, a comprehensive one on magic squares, Emperor Yu was supposedly strolling along the Yellow River one day around 2200 BC when he spotted the creature: its shell had a series of dots within squares. To Yu's amazement, each row of squares contained 15 dots, as did the columns and diagonals. When he added any two cells opposite along a line through the centre square, like 2 and 8, he always arrived at ten. 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 21st century, mathematicians would be studying magic squares so immense and in so many dimenstions that the objects defy ordinary human contemplation and visualization? Readers are treated to a colourful 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 should enjoy this encyclopedia of one of the few areas of mathematics where the contributions of even nonspecialists count.
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 book, a comprehensive one on magic squares, Emperor Yu was supposedly strolling along the Yellow River one day around 2200 BC when he spotted the creature: its shell had a series of dots within squares. To Yu's amazement, each row of squares contained 15 dots, as did the columns and diagonals. When he added any two cells opposite along a line through the centre square, like 2 and 8, he always arrived at ten. 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 21st century, mathematicians would be studying magic squares so immense and in so many dimenstions that the objects defy ordinary human contemplation and visualization? Readers are treated to a colourful 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 should enjoy this encyclopedia of one of the few areas of mathematics where the contributions of even nonspecialists count.
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.
Preface xi Acknowledgments xix Introduction 1 CHAPTER ONE: Magic Construction 37 CHAPTER TWO: Classification 65 CHAPTER THREE: Gallery I : Squares, Cubes, and Tesseracts 147 CHAPTER FOUR: Gallery 2: Circles and Spheres 297 CHAPTER FIVE: Gallery 3: Stars, Hexagons, and Other Beauties 325 Some Final Thoughts 369 Notes 375 For Further Reading 395 Index 397 About the Author 403
| Erscheint lt. Verlag | 6.1.2002 |
|---|---|
| Zusatzinfo | 191 line illus. |
| Verlagsort | New Jersey |
| Sprache | englisch |
| Maße | 152 x 235 mm |
| Gewicht | 765 g |
| Themenwelt | Sachbuch/Ratgeber ► Natur / Technik |
| Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Mathematik / Informatik ► Mathematik ► Mathematische Spiele und Unterhaltung | |
| ISBN-10 | 0-691-07041-5 / 0691070415 |
| ISBN-13 | 978-0-691-07041-4 / 9780691070414 |
| Zustand | Neuware |
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