# Chinese Counting Rods: Their History, Arithmetic Operations, and Didactic Repercussions

• Alexei Volkov
Chapter
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 11)

## Abstract

The chapter provides a history of Chinese counting rods (suan 算/筭) and a description of operations performed with them. The author discusses the representation of positive and negative numbers with counting rods of two colors or of two different cross-sections used in the procedure of solution of linear simultaneous equations described in the mathematical treatise Jiu zhang suan shu 九章筭術 (Computational Procedures of Nine Categories) completed no later than the early first century CE and explained in the commentary on it written by Liu Hui 劉徽 in 263. He also describes arithmetical operations performed with the counting rods mentioned in the mathematical treatise of the first millennium CE Sun zi suan jing 孫子筭經 (Master Sun’s treatise on computations) and in the treatise Shen dao da bian li zong suan hui 神道大編曆宗算會 (Grand Compendium of Divine Dao: [Chapters presenting methods] of lineages [of experts] in calendrical computations and of assembly of mathematicians [of the past]) completed by Zhou Shuxue 周述學 in 1558. The author claims that the “algorithmic style” of the traditional Chinese mathematics was intimately related with the use of the counting rods and that the transition from this instrument to the beads abacus (suanpan 算盤) that took place in the first half of the second millennium CE coincided with the general decline of Chinese mathematics.

## Keywords

History of Chinese and Japanese mathematics History of counting devices in China and Japan Chinese counting rods (suan 算/筭) Chinese algorithms for arithmetic operations Chinese beads abacus (suanpan 算盤)

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