Overview

The 4000 year- old mystery of Chinese magic squares is finally solved! Magic squares have fascinated ordinary and serious mathematicians alike for four thousand years. Great Yu discovered the first three by three magic square on the back of a turtle around the year 2200 B.C. before he was crowned the first emperor in China. Some three thousand years later in 1275, Yang Hui amused his countrymen with riddles describing the creations of third and fourth order magic squares. Two hundred forty years later in 1514, Albrecht Durer unknowingly applied Yang Hui's diagonal reversal scheme to produce in the Western world the first magic square. Some eighty years later in 1593, another Chinese mathematician Cheng Darwai produced a sixth-order magic square with a unique magic sum in every row, every column, but only in each of its twin diagonals knowns as the main and secondary diagonals. In this book, for the first time, F.Y. Chang has deciphered Yang Hui's riddles and extends both ancient Chinese mathematician's works and develops algorithms to create magic squares beyond the computation capacity of super computers. He formulates techniques such as parametric matrix formulation, row/column sum equalization, triple orthogonal transformation and diagonal switching for creation of the classical Chinese magic squares. He discovered the super diagonal Chinese magic squares with the magic sum in every generalized diagonal including the two conventional diagonals as well as an even number of four-segment split diagonals. Dr. Chang also introduces the idea of Chinese magic square games, which anyone of any age who is a number enthusiast can solve either by logical reasoning or by solving parametric linear equations.

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9781478780779

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