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Showing posts with label magic tori. Show all posts
Showing posts with label magic tori. Show all posts
Saturday, 14 September 2019

List of the 880 Frénicle Magic Squares of Order-4

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Bernard Frénicle de Bessy was the first to determine that there were 880 essentially different magic squares of order-4, and his findings...
Monday, 11 September 2017

Paired and Self-Complementary Magic Tori of Order-4

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In his paper "Self-complementary magic squares of 4x4," Mutsumi Suzuki has shown that there are 352 self-complementary magic squa...
Wednesday, 30 November 2016

Pandiagonality of the Squared Matrices of Associative and Related Magic Squares

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The present study is inspired by Miguel Angel Amela's paper dated September 2016, entitled "Powers of Associative Magic Squares,...
Saturday, 10 September 2016

Magic Torus Coordinate and Vector Symmetries

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Magic squares have fascinated mathematicians for centuries and they continue to do so today. However, many questions remain unanswered, and...
Monday, 29 August 2016

Complementary Number Patterns on Fourth-Order Magic Tori

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The 880 fourth-order magic squares were first identified and listed by Bernard Frénicle de Bessy in his « Table générale des quarrez magi...
Wednesday, 26 March 2014

Magic Diagonal Sequences of 4th-Order Magic Tori

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The number of fourth-order magic series is 86. The complete list of these magic series has been published by Walter Trump, who gave me con...
Thursday, 28 March 2013

1,920 Sub-Magic Squares on 255 4th-Order Magic Tori

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Further to my last article (published on the 26th March) Harry White has kindly run a computer programme to verify and validate my hy...
Tuesday, 26 March 2013

Sub-Magic 2x2 Squares on Fourth-Order Magic Tori

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My recent studies have shown that 2x2 sub-magic squares are fundamental in the way the fourth-order magic tori work. It has long been known...
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