A NEW METHOD FOR GENERATING MAGIC SQUARES OF SQUARES

THE USE OF ONE IMAGINARY NUMBER AS PART OF THE RIGHT DIAGONAL (Part IC)

Production of New Tables

This page continues from the previous Part IB. The next two tables employing numbers 288 and 289, respectively, are Tables XI and XII and the Sum of each tuple, i.e., every other line is:

shown at the extreme right and are both identical. Again we start off with either of these two numbers and fill up the tables by adding either 289 to 288 or 288 to 289 (with or without the is). The δs are incremented by 578 for Table XI and 576 for Table XII. The δs are then added to the previous a or c. The b is calculated as previously according to equation:

where n is in our first case either 288 or 289. I have placed an expanded version of the first two tuples of both 288 and 289 in Part IIC.

The light orange tuples of Table XI, whose numbers are all even, and therefore, factorable, by 4 as shown in the Table XI_{subset 1}. The difference between a and c, however, is now 144 compared to 576 for those tuples of Table XI. This former number while not belonging to the allowed numbers, i.e., (Δ_c-a = the difference between c and a, of the parent table, are allowed for the sub-tables. The tuples generated by these sub-tables provides, upon squaring, a greater number of tuples that can be used as the main diagonals in magic squares of squares.

This concludes Part IC. Go to Part IIIC to continue on tables of allowed tuples.

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