The central table in each of the nine sets is now our only concern. And all we do with each is add two numbers together.
In this example we may add any matching colour, for instance the top left hand corner added to the bottom right hand corner: 60 + 180 = 240. Each of the other matching colour combinations gives the same total of 240 (as do many more combinations that are not highlighted).
By referring to the tables in the previous Step, we find the totals from each of the nine Sets are as follows.
These are the nine numbers that we may arrange in the nine positions of the Luo Shu.
It is a magic square, and just as the rows, columns and diagonals of the Luo Shu add to its magic number of 15; each of the rows, columns and diagonals of this square derived from the He Tu add to 6,480.
Our mathematical journey is almost complete. From the He Tu, Paul Martyn McGowan has arrived at a magic square that may be regarded as a close relative of the Luo Shu. It enshrines some numbers of numerological significance that we shall briefly consider in the conclusion, and these numbers became the focus of Paul's attention.
I, however, noticed that the smallest number in the grid is 240 (derived from Set One), and that all of the numbers in the grid are actually divisable by this number. We can, therefore, reduce the size of the figures in the grid by dividing each by 240, as below, left.
This is also a magic square (magic number 27), and contains the first nine odd numbers. The numerical gap between each number is two which, when halved, gives us a numerical gap of one, which is the Luo Shu itself (above, right).
Conclusion
or return to the Second step (second time around)
© Ken Taylor 2006