See here. Also called the “de la Loubere” method. This was recently brought to my attention. I’d never heard of it before.
“A very simple method to construct any size of n-odd magic squares (i.e. number squares in which the sums of all rows, columns and diagonals are identical). The method was brought to France in 1688 by the French mathematician and diplomat Simon de la Loubère, as he was returning from his 1687 embassy to the kingdom of Siam. The Siamese method makes the creation of magic squares easy, without resort to guesswork.”
They look neat, kind of. Is there any sort of practical application for these, or are they just a puzzle?
You can use the Siamese method to create a compound magic square, as well, by dividing a 9x9 square into nine 3x3 squares. Start in the top-center square of the top-center 3x3 and count up to 9, staying inside the top 3x3… then go to the “number 2” 3x3 (lower left) and start in its top-center square with the number 10. I once filled in a 27x27 using this method, doubly-nested.
Other than a neat diversion that fills up a lot of graph paper, it’s not good for much. You can use it to teach some basic algebra skills with 5th and 6th graders, I guess, and leaving a little 3x3 or 5x5 on an office-mate’s whiteboard is sure to raise some eyebrows.