counting rod

mathematics

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June 24, 2026

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Counting rods were a crucial tool in ancient Chinese mathematics, particularly as described in The Nine Chapters. These rods, used on a counting board, represented numbers within a decimal place-value system. This system allowed for numbers to be easily manipulated and modified during calculations.12

The use of counting rods significantly influenced mathematical development. They were instrumental in performing fundamental arithmetic operations like addition, subtraction, multiplication, and division. Furthermore, they were used for more complex procedures, including finding square and cube roots, and solving quadratic equations. The ability to move and adjust numbers with rods facilitated the development of algorithms that are still recognizable today.12

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East Asian mathematics
The Nine Chapters
…the numbers were represented by counting rods (see the figure) that were used according to a decimal place-value system. Numbers represented by counting rods could be moved and modified within a computation. However, no written computations were recorded until much later. As will be seen, setting up the computations with…
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…the numbers were represented by counting rods (see the figure) that were used according to a decimal place-value system. Numbers represented by counting rods could be moved and modified within a computation. However, no written computations were recorded until much later. As will be seen, setting up the computations with…
Read More