Author Archives: Simon

Pythagoras and Agrippa

Of right triangles and odd squares 3^2 + 4^2 = 5^2 5^2 + 12^2 = 13^27^2 + 24^2 = 25^29^2 + 40^2 = 41^2…27^2 + 364^2 = 365^2…

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Lovely pattern T( 6) = 21T( 66) = 2211T( 666) = 222111T( 6666) = 22221111T( 66666) = 2222211111…

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Goetic Squares

Putting together the trigram and the hexagram squares we now have a complete set of 72 Goetic squares. It is left as an exercise to map each one to its corresponding demon.

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Hexagram or I Ching Squares

After the trigram squares, looking for a further transformation of the LuoShu, we can relax the constraint on the sum of the diagonals. This gives us 64 extra squares that could be mapped on the 64 hexagrams of the I … Continue reading

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Taijitu Transformations

Taijitu and LuoShu are symbols of balance and harmony. We can apply the same three basic transformations to the Taijitu as we did to the LuoShu: rotation, horizontal mirroring and vertical mirroring.

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Trigrams on a Square!

Let’s place the eight trigrams on a LuoShu square. First let’s associate the trigrams to a value according to their binary representation equivalent. We need nine numbers and zero was not much in use when the LuoShu was designed. So let’s … Continue reading

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Trigram Squares

The Luoshu layout follows the  traditional convention of chinese maps, where North is at the bottom and South at the top, so number one is drawn at the bottom center and number nine at the top center. Still, this is not … Continue reading

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Taijitu as a mnemonic for LuoShu

While the LuoShu (3×3 magic square) is simple to memorize by itself, one visual trick to remember the layout of the nine numbers is the Taijitu (yin-yang symbol). Write down the numbers from one to nine following the swirling pattern … Continue reading

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Asinus asinum fricat

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A riddle: I cast dices, pick dominoes, play roulette, draw tarot cards and mahjong tiles┬ábut always find┬áthe same numbers… … Triangular numbers. T( 3) = 6T( 7) = 28T( 8) = 36T( 12) = 78T( 16) = 136

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