A Latin Square is an array of symbols, (usually numbers) in a Square grid, where the symbols are arranged in such a way that each symbol occurs exactly once in each row and exactly once in each column.
One of the oldest known Latin Squares is the Sator Square. This Square was supposedly found amongst the ruins of Pompeii in the volcanic ashes resulting Mount Vesuvius in 79 AD, pressed in clay or carved in stone.
The Sator Square is an example of a palindromic, (reads the same way backwards) Latin Square.
The meaning behind Latin words in this Square has been subject to a debate. Loosely translated:
Sator, arepo, tenet, opera, rotas
“Arepo, the sower, preserves the wheels by his works”
Latin Squares were first used on amulets and talismans, as well as in rites in certain Arab and Indian communities, dating back to the year 1000. Most of these amulets contained not Latin Squares, but in fact magic Squares and were worn to fight evil spirits, show reverence for gods, and celebrate the sun and the planets.
The Arabic Mathematician Ahmad Al-Buni in and around the year 1200 wrote a book, which included a 7 x 7 Latin Square, depicting the Planet Jupiter and its day of the week in Thursday.
The Latin Squares of Al-Buni appear to have served two purposes; Firstly, to demonstrate certain magic powers with their relation to a specific ruling planet. Secondly, their crucial role in the construction of Magic Squares.
Al-Buni’s construction methods were adopted by Hindu mathematicians, as evidenced in a book from 1356 on Indian mathematics. The book references Latin Squares, with a clear focus on their use in certain constructions of Magic Squares. Hindu mathematics anticipated what Leonhard Euler in the 18th century later formalised and developed. The systematic development of Latin Squares started with Euler (1779) and was carried on by Cayley (1877-1890).