Counting rods are laid out to form numbers using decimal place value: the same rod, set in a different place, stands for a different number. Calculating this way replaced the earlier tally marks.
A Warring States tomb of Chu at Zuojiagongshan in Changsha has yielded neat bamboo rods, which shows that rod calculation in decimal place value was already used for practical sums.
Sunzi's Mathematical Manual, written around the Eastern Jin, records the rule for setting out numbers with rods: "one vertical, ten horizontal, a hundred upright, a thousand lying down".
Calculation with rods laid the basis for complex algebraic work of old such as root extraction and the tianyuan method. From the Ming the abacus gradually replaced the rods.
Counting Rods & Decimals is the class in the chapter on Sciences on calculating with counting rods in decimal place-value notation. The rods are slender bamboo sticks laid out on a table to record numbers and work sums; they replaced the earlier tally marks and laid the basis for more complex work such as root extraction and the tianyuan method, the method of the celestial element.
