## Magic Squares and CubesA magic square consists of a series of numbers so arranged in a square that the sum of each row and column and of both the corner diagonals shall be the same amount which may be termed the summation. In "Magic Squares and Cubes" W.S. Andrews writes "The study of magic squares probably dates back to prehistoric times. Examples have been found in Chinese literature written about AD 1125 which were evidently copied from still older documents. It is recorded that as early as the ninth century magic squares were used by Arabian astrologers in their calculations of horoscopes, etc. Hence, the probable origin of the term magic, which has survived to the present day." Topics such as magic squares, magic cubes, the Franklin squares, magics and Pythagorean numbers, the theory of reversions, magic circles, spheres, and stars, and magic octahedroids, among other things. |

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6X6 square 8X8 square arithmetical arithmetical sequence arithmetical series arranged associated magic square associated squares bers break-moves celt circles complete constructed contains the series corner cells corner diagonal columns couplets diagrams eight numbers equal equation example figures four numbers Franklin Franklin squares geometrical given in Fig horizontal increments initial number Jaina knight's move knight's tour last number left-hand magic cube magic rectangle middle Nasik number of cells numbers in Fig octahedroid odd magic squares odd numbers pairs of numbers pandiagonal parallel parallelepipeds placed cells plane diagonals Plutarch produce regular result reversion right-hand root square rows and columns rule Section sequence series of numbers shown in Fig square of order square shown subsquares summation symbols Tetractys Totals upper vertical squares Xasik

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Page viii - ... which reflects the symmetry of the divine norm immanent in all things, in the immeasurable immensity of the cosmos and in the construction of the atom not less than in the mysterious depths of the human mind.

Page vii - Bk. 1, chap. 1. 1603. Pythagoras says that number is the origin of all things, and certainly the law of number is the key that unlocks the secrets of the universe. But the law of number possesses an immanent order, which is at first sight mystifying, but on a more intimate acquaintance we easily understand it to be intrinsically necessary; and this law of number explains the wondrous consistency of the laws of nature.