Shabakh

Shabakh is a method of multiplication that uses a lattice, developed in India from the twelfth century onwards and seen in Hindu works. It can be used to multiply any two numbers.

Description

A grid is drawn up, and each box is split diagonally. The first and second numbers are positioned along the top and right of the lattice respectively, with each number being above a column, or next to a row. Simple products are written in each box, corresponding with numbers along the top and to the right of each box. For example, if the number above the box is 3, and the number to the right is 6, [1/8] (for 18) will be written in the box.

After all the boxes are filled in this manner, the diagonals are added from right to left, bottom to top, with the numbers added and written where the diagonal leads. Numbers are filled to the left and to the bottom of the grid, and the answer is the numbers read off down (on the left) and across (on the bottom).

Example

"58 x 213"

5 and 8 are written along the top of the lattice, and 2, 1 and 3 are written downwards to the right of the lattice. The two numbers corresponding to the box are multiplied and the result is put in the box: in the first box, 5 (from the top) is multiplied with 2 (from the right) to give 10, written in the grid as [1/0] .

Once each box has been filled, numbers are added diagonally. The 4, from the bottom right, is the only number in that diagonal, so it is written beneath the lattice. The 8, 2 and 5 are added (15), and the 5 is written beneath the lattice with the 1 being carried on to the next diagonal.

Once all the diagonals have been added, the answer is found by reading off the numbers downwards on the left (1, 2, 3) followed by the numbers along the bottom from left to right (5, 4), giving the answer of 12,354.