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This innovative work replaces magic square numbers with two-dimensional forms. The result is a revelation that traditional magic squares are now better seen as the one-dimensional instance of this self-same geometrical activity.
A funny, entertaining introduction to Ben Franklin and his many inventions, including the story of how he created the "magic square." A magic square is a box of nine numbers arranged so that any line of three numbers adds up to the same number, including on the diagonal! Teachers and kids will love finding out about this popular teaching tool that is still used in elementary schools today!
The science of magic squares witnessed an important development in the Islamic world during the Middle Ages, with a great variety of construction methods being created and ameliorated. The initial step was the translation, in the ninth century, of an anonymous Greek text containing the description of certain highly developed arrangements, no doubt the culmination of ancient research on magic squares.
Welcome to this fantastic collection of 100 magic square puzzles! Looking for a brain-teasing challenge? Look no further! Magic squares provide two key pieces of information for every puzzle; the sum of the numbers in each row, column and the two diagonals, and secondly the range of numbers that will feature, so 15-30 for example. With this information, you must completely fill the grid using the numbers already given in place. Can you complete all 100? If you get a little stuck along the way, solutions are featured towards the back of the book so take a peek there! All of our puzzle books are printed on very high quality paper, perfect for notes and scribbles! For other puzzle books, visit us at www.puzzle-book.co.uk
Within the pages of this book lies one of the most powerful mandalas of the Western Mystery Tradition. For the first time in English, Nineveh Shadrach has lifted the veil on a magic square whose properties astonished Magi of an age long past. They hid this square from the uninitiated with arcane terms such as the red sulfur and great elixir. They attributed its power to the rise of figures such as Alexander the Great. For hundreds of years advanced adepts of Western Occultism had no inkling of the existence of such a powerful magical artifact. Now you do. You'll expand your knowledge of authentic ancient sacred magic when you get: a) A partial translation of an ancient manuscript, revealing some of its secrets b) The blueprint for constructing this mandala of power to awaken its energy in your life c) Advanced teachings of esoteric numerology that shed light on its mysteries d) Ten additional variations, each designed to fully manifest the spiritual power of the emanations of the Tree of Life. This book is not for beginners or for those looking for quick fix spells. Anyone who has dug in hidden places in search of secret knowledge that can change lives will find a master key inside. All that is left is for you to use that key and unleash the ancient power of kings.
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.
Few American lives have been as celebrated--or as closely scrutinized--as that of Benjamin Franklin. Yet until now Franklin's biographers have downplayed his interest in mathematics, at best portraying it as the idle musings of a brilliant and ever-restless mind. In Benjamin Franklin's Numbers, Paul Pasles reveals a side of the iconic statesman, scientist, and writer that few Americans know--his mathematical side. In fact, Franklin indulged in many areas of mathematics, including number theory, geometry, statistics, and economics. In this generously illustrated book, Pasles gives us the first mathematical biography of Benjamin Franklin. He draws upon previously unknown sources to illustrate Franklin's genius for numbers as never before. Magic squares and circles were a lifelong fascination of Franklin's. Here, for the first time, Pasles gathers every one of these marvelous creations together in one place. He explains the mathematics behind them and Franklin's hugely popular Poor Richard's Almanac, which featured such things as population estimates and a host of mathematical digressions. Pasles even includes optional math problems that challenge readers to match wits with the bespectacled Founding Father himself. Written for a general audience, this book assumes no technical skills beyond basic arithmetic. Benjamin Franklin's Numbers is a delightful blend of biography, history, and popular mathematics. If you think you already know Franklin's story, this entertaining and richly detailed book will make you think again.
