Magic squares in India

Abstract

A square containing an equal number of cells in each row and each column is called a magic square, when the total of numbers in the cells of each row, each column and each diagonal happens to be the same. Magic squares have been known in India from very early times. It is believed that the subject of magic squares was first taught by Lord Śiva to the magician Maṇibhadra. Magic squares are said to have magical properties and were used in various ways by the Hindus as well as the Jainas. But the mathematics involved in the construction of magic squares and other magic figures was first systematically and elaborately discussed by the mathematician Nārāyaṇa (ad 1356) in his Gaṇitakaumudī. Some of his methods were unknown in the west and were recently discovered by the efforts of several scholars. The present article, besides giving a brief history of magic squares, explains the methods given by Nārāyaṇa and other Hindu writers for the construction of magic squares of various types.