Magic Squares and Cubes

A 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.