The ancient maths of ‘The Book of Changes’ is simple, and because of its simplicity it is not obvious unless the texts attributed to the lines of the Hexagrams are studied fully. Firstly one has to comprehend the meaning of the terms Heaven and Earth, as these are said to be the father and mother or the ‘Original Trigrams’. The trigrams are made-up of 3 binary lines, Heaven is 3 unbroken lines, Earth is 3 broken lines, and so they signify a singularity, and duality, and these give The Judgments and Law.

 

The 2 ‘Original Trigrams’ when combined make a further 6 trigrams called the children, and so all 8 have a placement in sequence when the ‘Original Trigrams’ are placed into natural integers from 1 to 10. This arrangement can be seen in Wilhelm’s edition of the I Ching on page 308, and the 2 River Maps into which these trigrams must be fitted follow on pages 309/10. The first of the River Naps is called the Yellow River Map and it is a simple arrangement of integers, as pairings, in the directions of the compass:

 

 

When the trigrams of Heaven and Earth are placed together in the directions of the map, the 8 trigrams are then doubled or squared to produce an 8 x 8 square, and so there are a total of 4 squares in the outer directions of the map.

 

 

As the trigrams manufacture the hexagrams or cubes all are placed into the square symmetrically, so all pairs have a common or central value. This applies to each square and then to all of the 4 squares, so that across all the 4 squares a central square of values is produced in the 5th central square of Earth.

 

 

This applies to each square and then to all of the 4 squares, so that across all the 4 squares a central square of values is produced in the 5th central square/circle of Earth

 

The amount of values in the Yellow River Map are 40 light and 40 dark, so between them they produce 8 x 8 x 8 hexagrams, or 8 x 5 central squares, which then fit into the second River Map called the Lo River Map or Lo Shu also know as the Magic Square of Saturn/Cronus the God of Time.

The 40 light and 40 dark values are: (please note value of 9 should read 54 not 52)

 

 

As the value of 1 went to 6 in the first set of values this progresses by 10’s, so in the second line Heaven 11 goes with Earth 16, and so on. When all the central squares have been found and fitted into the Lo Shu the total amount of light hexagrams = 12,960, and dark = 12,960, so a total value of 25,920 is found, and this = Precession. If the values of 5 and 10 are included then we get a 9 x 9 square, see Square of the Moon blog page.

 

The Lo Shu and Magic Square of Nine:

 

The maths here is just the basic workings, as there are so many aspects to it. I would advise anyone interested further to either download a free copy of my book, or just to start putting the values together for yourselves. Good hunting for all the many things one can find in Hexagrams.