Monday, 25 March 2013

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:

order 4 partially pandiagonal magic torus index T4.098 type T4.04.2
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:

order 4 line path partially pandiagonal magic torus type T4.04.2

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:

order 4 partially pandiagonal magic torus index T4.098 cross-sections 1


order 4 partially pandiagonal magic torus index T4.098 cross-sections 2

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

order 4 partially pandiagonal magic torus index T4.098 square patterns 1


order 4 partially pandiagonal magic torus index T4.098 square patterns 2

order 4 partially pandiagonal torus index T4.098 square patterns 3

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