Magic Squares, Spheres and Tori

Magic Squares offer partial glimpses of the convex or concave number systems that they represent. Analysed using modular arithmetic, Magic Tori open new perspectives.

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Showing posts with label semi-magic. Show all posts
Showing posts with label semi-magic. Show all posts
Thursday, 15 June 2023

440 Torus-Opposite Pairs of the 880 Frénicle Magic Squares of Order-4

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Finding the torus-opposite pairs of magic squares in even-orders: The following diagram, which illustrates the array of n² essentiall...
Monday, 2 September 2019

Even and Odd Number Patterns on Magic Tori of Orders 3 and 4

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Ancient references to the pattern of even and odd numbers of the 3 × 3 magic square appear in the "I Ching" or "Yih King...
Thursday, 9 March 2017

Perimeter Magic Squares

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After the first discoveries of area magic squares , I decided to do some more exploring and search for examples of perimeter magic squares. ...
Friday, 28 September 2012

251,449,712 Fifth-Order Magic Tori

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After finding the number of 3rd and 4th-order magic tori it was tempting to look further and Walter Trump kindly offered his computing sk...
Friday, 9 March 2012

From the Magic Square to the Magic Torus

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This post is a translation of the article "Passage du Carré Magique au Tore Magique," first published in French on the 11th Novem...
Monday, 9 January 2012

255 Fourth-Order Magic Tori, and 1 Third-Order Magic Torus

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This post is a translation of the article "255 Tores Magiques d'Ordre 4, et 1 Tore Magique d'Ordre 3," first published in ...
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