Counting rods

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Counting rods (simplified Chinese: ; traditional Chinese: ; pinyin: chóu; Japanese: 算木, sangi) are small bars, typically 3–14 cm long, used by mathematicians for calculation in China, Japan, Korea, and Vietnam. They are placed either horizontally or vertically to represent any number and any fraction.

The written forms based on them are called rod numerals. They are a true positional numeral system with digits for 1-9 and later also for 0.



Counting rods were used by ancient Chinese for more than two thousand years. In 1954, forty-odd counting rods of the Warring States Period were found in Zuǒjiāgōngshān (左家公山) Chǔ Grave No.15 in Changsha, Hunan.[1] [2].

In 1973, archeologists unearthed a number of wood scripts from a Han dynasty tomb in Hubei, one of the wooden script written:“当利二月定算Counting rod v6.png”,this is one of the earliest examples of using counting rod numeral in writing.

In 1976, a bundle of West Han counting rods made of bones in was unearthed from Qian yang county in Shanxi [3] The use of counting rods must predate it; the Laozi, a text originating from the Warring States, said "a good calculator doesn't use counting rods."[4] The Book of Han recorded: "they calculate with bamboo, diameter one fen, length six cun, arranged into a hexagonal bundle of two hundred seventy one pieces."

After the abacus flourished, counting rods were abandoned except in Japan, where rod numerals developed into symbolic notation for algebra.

Using counting rods

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