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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!
A story book for all ages to experience mathematics, problems solving, and the rewards that come with perseverance."Long ago in the land of China, there were many rain storms ... and the land of China was slowly sinking into the sea. This is the story of how a wise emperor, an observant girl, and a magic turtle saved the villages of China from the great flood." So begins the story of Ying and the Magic Turtle. Children ages 5 and up, parents, and teachers can enjoy the book for its rich beauty in mathematics and as an ancient legend. It is the kind of story to revisit over and over again.This book is perhaps best experienced with someone, as a read-aloud or read-together. When reading, we learn of Ying's trouble, and we root for her to find her solution. We find ourselves drawn into the life problems that Ying is facing, but also drawn into the inherent mathematics of the story. It is through the beauty of the pattern of the dots on the turtle's shell that the solution is finally found and the land is saved.We can appreciate each scene as we read, and then pause and predict what might come next. We can play with the mathematics, solving right alongside Ying. We can delve deeper into the power of magic squares by working with puzzles presented at the end of the story. There are unsolved problems in number theory even a young child can try, such as finding all the possible magic squares of a given size.
Traditional magic squares employ a chessboard-like arrangement of numbers in which the total of all rows, columns, and diagonals add up to the same number. This innovative approach by a Dutch engineer challenges puzzlists to think two dimensionally by replacing numbers with colorful geometric shapes. Dozens of creative puzzles, suitable for ages 12 and up.
Presents the development of Chinese urbanism. Equipped with source material and maps, this book applies metrological methods. Including about 300 drawings, it gives an overall view of the urban life and culture that existed in the traditional society of late Imperial China.
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.
Examines the unique combinations of numbers that make up magic squares, and describes an ancient magic square and one developed by Benjamin Franklin.
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.