Counting rods

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

The written forms based on them are called rod numerals. They are a true positional numeral system with digits for 1–9 and a blank for 0, from the Warring states period (circa 475 BCE) to the 16th century.

History

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.

In 1973, archeologists unearthed a number of wood scripts from a Han dynasty tomb in Hubei. On one of the wooden scripts was written: “当利二月定算”. This is one of the earliest examples of using counting rod numerals in writing.

In 1976, a bundle of West Han counting rods made of bones was unearthed from Qian Yang county in Shanxi. The use of counting rods must predate it; Laozi (6th or 5th century BCE) said "a good calculator doesn't use counting rods". 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". At first calculating rods were round in cross section, but by the time of the Sui dynasty triangular rods were used to represent positive numbers and rectangular rods were used for negative numbers.