Saturday, 23 March 2013

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:

order 4 magic torus index T4.001 normalised form type T4.05.1.02

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

order 4 line path magic torus index T4.001 type T4.05.1.02

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:
order 4 magic torus index T4.001 cross-sections 1
order 4 magic torus index T4.001 cross-sections 2

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

order 4 magic torus index T4.001 square patterns 1

order 4 magic torus index T4.001 square patterns 2

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