Rod calculus or rod calculation was the mechanical method of algorithmic computation with counting rods in China from the Warring States to Ming dynasty before the counting rods were increasingly replaced by the more convenient and faster abacus. Rod calculus played a key role in the development of Chinese mathematics to its height in Song Dynasty and Yuan Dynasty, culminating in the invention
of polynomial equations of up to four unknowns in the work of Zhu Shijie.
Japanese counting board with grids
Rod calculus facsimile from the Yongle encyclopedia
Representation of the number 231 and possible misleading rod placements.
Tian yuan shu in Li Zhi:Yigu yanduan
Counting rods (筭) are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient East Asia. They are placed either horizontally or vertically to represent any integer or rational number.
Toán trù 算籌 (counting rods) in a Vietnamese mathematics textbook, Cửu chương lập thành toán pháp 九章立成算法 is shown at the bottom of the page.
Rod numeral place value from Yongle Encyclopedia: 71,824
Japanese counting board with grids
A checker counting board diagram in an 18th-century Japanese mathematics textbook