Rod calculus

Rod calculus, also called rod calculation, was the mechanical method of algorithmic computation that Chinese mathematicians carried out with counting rods, from the Warring States period to the Ming dynasty, until the abacus gradually replaced it. Calculators laid rods of bamboo, bone, ivory or jade on a counting board or any flat surface to form rod numerals, a decimal positional system in which a blank space stands for zero and neighbouring places alternate between vertical and horizontal strokes so that digits are not misread. The only part learned by heart was the 45 phrase nine-nine multiplication table. Addition and subtraction work by physically moving rods, with no addition table needed, and carrying and borrowing follow fixed procedures that run from left to right. The method carried Chinese mathematics to its height in the Song and Yuan dynasties, culminating in Zhu Shijie's work on polynomial equations of up to four unknowns. Bundles of counting rods unearthed from Han dynasty tombs, including a bone bundle found in 1971 in Shanxi province, are the earliest physical remains.