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 n° T4.098 type n° 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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