Siamese method

The method was brought to France in 1688 by the French mathematician and diplomat Simon de la Loubère,[1] as he was returning from his 1687 embassy to the kingdom of Siam.

[2][3][4] The Siamese method makes the creation of magic squares straightforward.

De la Loubère published his findings in his book A new historical relation of the kingdom of Siam (Du Royaume de Siam, 1693), under the chapter entitled The problem of the magical square according to the Indians.

[5] Although the method is generally qualified as "Siamese", which refers to de la Loubère's travel to the country of Siam, de la Loubère himself learnt it from a Frenchman named M.Vincent (a doctor, who had first travelled to Persia and then to Siam, and was returning to France with the de la Loubère embassy), who himself had learnt it in the city of Surat in India:[5] "Mr. Vincent, whom I have so often mentioned in my Relations, seeing me one day in the ship, during our return, studiously to range the Magical Squares after the method of Bachet, informed me that the Indians of Suratte ranged them with much more facility, and taught me their method for the unequal squares only, having, he said, forgot that of the equal"The method was surprising in its effectiveness and simplicity: "I hope that it will not be unacceptable that I give the rules and the demonstration of this method, which is surprising for its extreme facility to execute a thing, which has appeared difficult to our Mathematicians"First, an arithmetic progression has to be chosen (such as the simple progression 1,2,3,4,5,6,7,8,9 for a square with three rows and columns (the Lo Shu square)).

[6] These variations, although not quite as simple as the basic Siamese method, are equivalent to the methods developed by earlier Arab and European scholars, such as Manuel Moschopoulos (1315), Johann Faulhaber (1580–1635) and Claude Gaspard Bachet de Méziriac (1581–1638), and allowed to create magic squares similar to theirs.