Abstract:
The magic square of eight can be formed in two ways, which may be called arithmetical and algebraic. In the former case the ordinary square of eight is fractioned into series parallel to the two diagonal series. Half of these are retained as such in the magic square, the other half are inversed, but order of numbers remains as before. This completes the transformation of the ordinary into its magic square of 8. The algebraical method starts with minimum data, with only that information which is implied in the term, "Magic square of eight. " The Right Diagonal, RD, begins with 1 and ends with 8; with the second item it takes "N" for 8, and "N" keeps increasing till it ends as (7N). Thus RD begins with (1) and ends with (7N + 8). The Left Diagonal LD, begins with N(N = 8), which increases with the 3rd item, finally ending as (7N). With the second item it takes (7) as additive which keeps decreasing till it becomes 1. LD then begins as (N) and ends as (7N + 1). It is shown to be an integration of opposites which are well balanced. The theory is that numbers potentially are powers, but union of opposites generates auspicious energy, making the design a charm with talismanic properties. Figures are offered to show how balanced opposite can make the design symmetrical. The items required to construct the magic square are indicated primarily by items of the diagonal series. Thus the formation of the final design is shown part by part. Algebrical items have been offered with keys to make the contents obvious. In the Magic Square of 8, each line now contains four odd numbers and four evens revealing proper balance.
Page(s):
361-378
DOI:
DOI not available
Published:
Journal: Proceedings of Pakistan Academy of Sciences, Volume: 27, Issue: 4, Year: 1990