Creating the mass model led to the discovery of some new properties .. such as the moment of inertia by Peter Loly. The model also lends itself to degenerating the square to one dimension and looking at its balance in one dimension across the midline
Figure 1 above … shows the distance from center values for the degenerated order 3 square
Shows the 4 possible degenerations for the order 3 square …
Ie read left to right, right to left, top to bottom, and bottom to top
Figure 3 above …
I wrote a program to search for all order 3 squares where the only criteria was
That the sum of the mass x distance totals had to be equal for the square for
All four possible degenerations ..
Two unique examples other than the standard
Magic square structure are found.
The pattern can be extended for higher order of squares but no interesting
Patterns emerge ( Francis Gaspalou)
All magic squares still balance across the midline when degenerated to one dimension.
Figure 4 above …
I have a continued interest in looking at exchanging distance and cell value units for the square.