The Science of the Shulba: A Study in Early Hindu Geometry c15.42

c15.42

It will be very interesting to know how the early Hindus discovered their rational rectangles. Thibaut observes : " Most likely they discovered that the square on the diagonal of an oblong, the sides of which were equal to three and four, could be divided into twenty-five small squares, sixteen of which composed the square on the longer side of the oblong, and nine of which formed the area of the square on the shorter side. Or, if we suppose a more convenient mode of trying, they might have found that twenty-five pebbles or seeds, which could be arranged in one square, could likewise be arranged in two squares of sixteen and of nine. Going on in that way they would form larger squares, always trying if the pebbles forming one of these squares could not as well be arranged in two smaller squares. So they would explained by the fact that the process of construction really began with a square consisting of 4 bricks. Next square was constructed by placing 5 squares, along its two sides, so that it contained 9 bricks. Proceeding thus and placing the additional bricks alternately on the north and east sides, and on the south and west sides, a square of 256 bricks was constructed without disturbing the position of symmetry of the altar about the east-west line. But the addition of the remaining 33 bricks displaced this symmetry and for this reason perhaps, Baudhāyana gave that unusual direction.¹