WEEKLY WHINE

But who’s multiplying: Rod calculus

Do you have rods lying around? Have you not built your abacus yet? Would you like something fun to do whilst you’re trying to figure out how large a variety of rectangular shapes are? Then rod calculus is for you. Sun Zi’s Calculation Classic, written in the fourth century AD, documented a variety of computations with Chinese rods. These examples are adapted from Sun Zi’s methods but are represented with Arabic numerals.

We start by lining up the last digit of the second multiplicand beneath the first digit of the first. Then we multiply the second multiplicand by the first digit of the first and place the result in the middle, aligned with the second multiplicand. The second multiplicand is shifted, and the product with the next digit of the first multiplicand is added in. We then continue shifting and adding the whole way down.

As you will note, this is equivalent to long multiplication, but the running totals are kept as the product moves along. It does, however, mean that if one was to do it with a pencil and paper, the process would be equivalent to long multiplication anyway.

But this is a good way to do rough multiplication, since the process starts with the most significant digits. Furthermore, if your Monopoly houses are still around from the peasant multiplication we did last week, you’ll likely find that this is a faster and more expandable method.