Information about Counting Rods

Counting rods (Traditional Chinese: 籌; Simplified Chinese: 筹; Pinyin: chou2) were a numeral system using only two symbols (horizontal bar and vertical bar) to represent any number and any fraction. Counting rods were used by ancient Chinese for more than a thousand years from the Shang dynasty to the Ming dynasty for calculation with rods before the invention of the abacus. The way that a number is presented by counting rods is called the rod numeral system. The rod numeral system is a decimal place value system, where the digits 1 to 9 are represented by a combination of horizontal and vertical bars. Each digit can be represented in two ways, vertically or horizontally, depending on the placing of the number.

The choice of vertical form or horizontal form depends on the position of each digit. For example, in the diagram at left, 231 is represented by a vertical 2, a horizontal 3, and a vertical 1. In general, vertical rod numbers are used for the position for the units, hundreds, ten thousands, etc., while horizontal rod numbers are used for the tens, thousands, hundred thousands etc. The purpose of this alternating use of vertical and horizontal forms is to avoid confusion. For instance, if 231 is represented entirely by vertical rod forms, as in the upper row in the diagram, then on a gridless counting board, the number 231 may be misread as 51, 24, 1211 etc. The ancient Chinese used red rods for positive numbers and black rods are for negative numbers. The method for using counting rods for mathematical calculation was called rod calculation or rod calculus (筹算‎).

Rod calculus can be used for a wide range of calculations, including finding the value of π, finding square roots, cube roots, or higher order roots, and solving a system of linear equations. As a result, the character 籌 is extended to connote the concept of planning in Chinese. For example, the science of using counting rods 運籌學 does not refer to counting rods; it means operational research.

Before the introduction of 0, there was no way to separate 10007 and 107 except by inserting a bigger space between 1 and 7, and so rod numerals were used only for doing calculations with counting rods. Once 0 came into play, the rod numerals had become independent, and their use indeed outlives the counting rods. One variation of horizontal rod numerals is still in use for book-keeping in Chinatowns in some parts of the world (see the article on Chinese numerals).

See also

• Rod calculus
• Abacus
• Chinese mathematics

External links

For a look of the ancient counting rods, and further explanation, you can visit the sites:

• http://www.math.sfu.ca/histmath/China/Beginning/Rod.html
• http://mathforum.org/library/drmath/view/52557.html
• http://big5.ce.cn/gate/big5/cathay.ce.cn/history/200612/05/t20061205_9676970.shtml