The Science of the Shulba: A Study in Early Hindu Geometry c19.s2.7

c19.s2.7

Now it may be asked how the ancient altar-builders determined the size of the bricks of different kinds and the number of bricks of each kind that will be required for the construction of each layer. They proceeded probably in some way like this: Since 21 is not a square number, no layer of the altar can be constructed with bricks of the same kind. So the number of kinds of bricks employed in any layer must be at least 2. Since no two successive layers should have identical cleavage, all the bricks employed in the second layer must not be the same as those of the first layer. Hence the minimum kinds of bricks must be 3. Assume then their sides to be *p*, *q* and *r*th part of a vyāyāma, where *p*, *q*, *r* are rational integers to be determined. Suppose the first layer consists of *x* bricks of the first kind and *y* bricks of the second kind. Then we must have $x/(p²) + y/(q²) = 1,$ $x + y = 21.$