Connections between Latin Squares and Geometries

Abstract

The present paper deals with Latin squares, orthogonal Latin squares, mutually Orthogonal Latin squares, close connections between Latin squares and finite geometries. Moreover the great mathematician Leonhard Euler introduced Latin squares in 1783 as a nouveau espece de carres magiques, a new kind of magic squares. He also defined what he meant by orthogonal Latin squares, which led to a famous conjecture of his that went unsolved for over 100 years. In 1900, G. Tarry proved a particular case of the conjecture. It was shown in 1960 by Bose, Shrikhande, and Parker that, except for this one case, the conjecture was false.