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The nine Indian planetary magic squares of order 3 are attributed to Garga, who is said to belong to the hoary past. Formation of magic squares of order 9 from those of order 3, as bimagic squares, is found both in India and China. BhuvaneœvarÁ yantra is a bimagic square of order 8. Its full Sanskrit text, along with translation and the method of construction is described in the present paper. Construction of bimagic squares of orders 8 and 9 from simple orthogonal Latin squares is dealt with in detail. Recalling that Euler’s conjecture on Latin squares has been disproved, a counter-example of order 10 is described. [ABSTRACT FROM AUTHOR]

Design Theory, a branch of mathematics, was born out of the experimental statistics research of the population geneticist R A Fisher and of Indian mathematical statisticians in the 1930s. The field combines elements of combinatorics, finite projective geometries, Latin squares, and a variety of further mathematical structures, brought together in surprising ways. This essay will present these structures and ideas as well as how the field came together, in itself an interesting story. [ABSTRACT FROM AUTHOR]