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 n° T4.001 (type n° 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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