Fourth-Order Partially Panmagic Torus T4.098

As shown in previous articles, the partially panmagic squares with Frénicle index n°275 and 519 are displayed on a same partially panmagic torus classified by type T4.04.2, and indexed (using normalised torus form) T4.098.

When studied on the surface of the partially panmagic torus we are not able to begin the line path as there are two ways round the torus ring to link 1 with 2:

In order to better visualise how the T4.098 partially panmagic torus works I have produced the diagrams below. The partially panmagic torus is a symmetrically stable number system. Different number couples produce continuously balanced tensions. I have indicated some of the mathematical properties but you will notice others when you contemplate this beautiful counting machine:

The number couples of the partially panmagic torus produce different patterns on the magic squares that they display:

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Fourth-Order Magic Torus T4.001

As shown in previous articles, the basic magic squares with Frénicle index n°002 and 448 are displayed on a same magic torus classified by type T4.05.1.02, and indexed (using normalised torus form) T4.001.

When studied on the surface of the magic torus, the line path between consecutive numbers is completely different to that of the magic square :

In order to better visualise how the T4.001 magic torus works I have produced the diagrams below. The magic torus is a symmetrically stable number system. Different number couples produce continuously balanced tensions. I have indicated some of the mathematical properties but you will notice others when you contemplate this beautiful counting machine:

The number couples of the magic torus produce different patterns on the magic squares that they display:

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