Magic Square is no longer magic, but the era of magic square puzzle has just begun. This outstanding application of Magic Square will be played by millions throughout the world. I appeal to educators to adopt magic square puzzles to schools' curriculums. If you are interested, e-mail me at dwkmei@aol.com.
Magic Square
Its New Discoveries and Applications
By David MeiAuthorHouse
Copyright © 2015 David Mei
All rights reserved.
ISBN: 978-1-5049-1837-4Contents
I. Magic Square Before Our Time p., 1-3,
II. The Construction Of A Magic Square,
A) 3 X 3 MAGIC SQUARE, p. 4,
B) 4 X 4 MAGIC SQUARE, p. 5-6,
C) 5 X 5 MAGIC SQUARE, p. 7-8,
D) 6 X 6 MAGIC SQUARE, p. 9,
E) 7 X 7 MAGIC SQUARE, p. 10,
F) 8 X 8 MAGIC SQUARE, p. 10,
G) 9 X 9 MAGIC SQUARE, p. 11,
H) 10 X 10 MAGIC SQUARE, p. 12,
I) 11 X 11 MAGIC SQUARE, p. 13,
J) 12 X 12 MAGIC SQUARE, p. 14-17,
K) MAGIC SQUARE BEYOND 12 X 12, p. 18-19,
L) SUMMARY, p. 20,
III. The Discovery Of Mel's Square Method,
A) BASE, p. 21,
B) THE ARRANGEMENT OF NUMBERS, p. 21,
C) MEI'S SQUARE, p. 22-25,
IV. The Applications Of Magic Squares,
A) THE EXTENSION OF KNIGHT'S MOVE METHOD, p. 26-27,
B) MAGIC SQUARE PUZZLE, p. 28-33,
C) THE GAME OF 24, p. 34,
V. Magic Square Now And Beyond, p. 35,
CHAPTER 1
Magic Square Before Our Time
A magic square is merely a group of numbers arranged in a fancy way. Its existence dates back to ancient time. Philolaus once has said, "Number is the bond of the eternal continuance of thing." The mysterious relationships of numbers have occupied the minds of men in all ages through centuries since men incept numbers for simple counting to complicated calculations. The study of numbers becomes hit-parade those days and attributes the birth of magic squares. A square is called magic, only if the sum of numbers in each of its rows, columns and diagonals adds up to a same amount.
One of the oldest magic square in the East is the Chinese Scroll of Loh attributed to Fuh-Hi, the mythical founder of Chinese civilization, who according to Chinese report lived 2858-2738 B.C.. The Scroll of Loh is a 3x3 magic square: all the odd numbers in white dots are the symbol of Yang, the emblem of heaven, while the even numbers in black dots are the symbol of Yin, the emblem of the earth. Same as to their Eastern counterpart, the magic squares are only associated with astrologers, magicians and talisman makers in the West, not until the mathematical value of magic square has been justified. From a paper entitled "Magic Squares and Other Problems on a Chessboard" by Major P.A. Mac Mahon, R.A., D. Sc., F.R.S., published in Proceedings of the Royal Institute of Great Britain, in 1892, he concludes that the magic square is intimately connected with the infinitesimal calculus and the calculus of finite differences.
So, the study of magic square becomes the hottest subject for philosophers, mathematicians and the pass time for the noble class who can afford the time and the luxury in Europe. However, they end up finding a very difficult time in constructing new magic squares. In late 19th century, W.S. Andrew, a famous mathematician from England, writes in his book Magic Squares and Cubes that, "Many attempts have been made to construct magic squares from a natural series of numbers by locating each succeeding number a Knight's move from the last one, until every call in the square is included in one continuous Knight's tour. This difficult problem however has never been solved, and the square in question probably does not exist. Many squares have been made that sum correctly in their lines and columns, but they all fail in their two diagonals and therefore are not strictly magic." He also confirms that the construction of magic squares become laborious.
Nevertheless, the general public take it as a golden opportunity for them
