THE TWO MAGIC SQUARES OF SEVEN SQUARES

SQUARES DERIVED FROM THE SAME PRESQUARE

Andrew Bremner's article on squares of squares included the 3x3 square:

Bremner does not state where the numbers in the right diagonal (205²,425²,565²) were derived. However, I will show that the diagonal numbers are derived from a set of tuple numbers, i.e. the nonsquare numbers, (41,85,113) multiplied by a constant k, as shown in the simple presquare below:

where the Bremner square is obtained from the presquare by multiplying the tuple numbers by the constant k = 5 and the new square by multiplying the tuple numbers by the contant k = 6. In addition, the new square is composed of both regular and imaginary numbers, where the square of an imaginary number is a negative number. Attempts to generate other 7 squares other than those produced from the constant k equal to 5 or 6 either gave multiples of the same two squares or failed to produce new squares. This is in opposition to four other squares of seven squares containing a mixture of regular and imaginary numbers where the initial number in the diagonal is an imaginary number.

Go back to homepage.