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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.
This collection of essays spans pure and applied mathematics. Readers interested in mathematical research and historical aspects of mathematics will appreciate the enlightening content of the material. Highlighting the pervasive nature of mathematics today in a host of different areas, the book also covers the spread of mathematical ideas and techn
This book contains a series of research notes and graphical illustrations selected from the author’s amazing research work. It shows how: · The Sixty-Four hexagrams were derived by using combinatory trigrams selected from the Earlier Heaven and Later Heaven trigram cyclic sequences. · The legendary authors of the I Ching, known as Fu Hsi and King Wen, used Key Coded Matrices which enabled them to change the hexagrams of the ancient Ma-wang-tui into the Standard Modern edition. · The formulation of the Trigram Order of Completion was derived by using Knight’s Chess /binary codes and the manipulation of hexagram identification numbers. · The cyclic sequences and trigram line to line transitions were utilized to formulate the King Wen’s hexagram arrangement. · The natural numerical notation for each individual trigram was mathematically derived. · The author’s inter-face code was derived and used to determine the mathematical methodology of the Genetic Code. · Trigram lines are manipulated to form the Inner and Outer Nuclear trigrams/ hexagrams. · The Genetic Code was determined from Fu Hsi’s diagram of the derivation of the Sixty-Four hexagrams. It also includes the constructional details of an analytical model calculator which can be created from the actual design details shown within this book. This document provides the conclusive evidence that the originator(s) of the I Ching used a mathematical system which encompassed a formalistic natural philosophy that sought to embrace the entire world in a system of number symbolism. It shows the links to the ancient Indian Vedic mathematical system which reveals the relationship between the I Ching and the Binary / Genetic Codes.
This book includes 58 selected articles that highlight the major contributions of Professor Radha Charan Gupta—a doyen of history of mathematics—written on a variety of important topics pertaining to mathematics and astronomy in India. It is divided into ten parts. Part I presents three articles offering an overview of Professor Gupta’s oeuvre. The four articles in Part II convey the importance of studies in the history of mathematics. Parts III–VII constituting 33 articles, feature a number of articles on a variety of topics, such as geometry, trigonometry, algebra, combinatorics and spherical trigonometry, which not only reveal the breadth and depth of Professor Gupta’s work, but also highlight his deep commitment to the promotion of studies in the history of mathematics. The ten articles of part VIII, present interesting bibliographical sketches of a few veteran historians of mathematics and astronomy in India. Part IX examines the dissemination of mathematical knowledge across different civilisations. The last part presents an up-to-date bibliography of Gupta’s work. It also includes a tribute to him in Sanskrit composed in eight verses.