The counting rods (Traditional Chinese: 籌, Simplified Chinese: 筹, pinyin: chou2) were used by ancient Chinese 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 in two ways: Traditional Chinese characters are one of two standard character sets. ... Simplified Chinese characters (Simplified Chinese: 简体字; Traditional Chinese: 簡體字; pinyin: jiÇŽntǐzì; also Simplified Chinese: 简化字; Traditional Chinese: 簡化字; pinyin: jiÇŽnhuàzì) are one of two standard character sets of printed contemporary Chinese written language. ... Pinyin is a system of romanization (phonemic notation and transcription to Roman script) for Standard Mandarin, where pin means spell and yin means sound. The most common variant of pinyin in use is called Hanyu Pinyin (Simplified Chinese: , Traditional Chinese: ; pinyin: HànyÇ” PÄ«nyÄ«n), also known as scheme... An abacus is a calculation tool, often constructed as a wooden frame with beads sliding on wires. ...

Image File history File links Chinese rod numerals -- wshun 14:49, 14 Dec 2004 (UTC) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...

depending on their positions. For example 126 is represented by |=⊤ instead of |∥⊤ which could be confused with 36. Usually red rods are for positive numbers and black rods are for negative numbers.

The counting rods could be used for a wide range of calculations, including finding the value of π and solving system of linear equations. As a result, the character 籌 is commonly associated with the concept of planning in Chinese. For example, the science of using counting rods 運籌學 is not about the counting rods: it means operational research. When a circles diameter is 1, its circumference is Ï€. The mathematical constant Ï€ is an irrational real number, approximately equal to 3. ... In mathematics and linear algebra, a system of linear equations is a set of linear equations such as 3x1 + 2x2 − x3 = 1 2x1 − 2x2 + 4x3 = −2 −x1 + ½x2 − x3 = 0. ... Operations research, operational research, or simply OR, is the use of mathematical models, statistics and algorithms to aid in decision-making. ...

Before the introduction of 0, there was no way to separate 10007 and 107 except 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 rod numerals is still in use, see the article on Chinese numerals. Because of technical limitations, some web browsers may not display some special characters in this article. ...

For an example, see Yang Hui's triangle. 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 The first six rows of Pascals triangle In mathematics, Pascals triangle is a geometric arrangement of the binomial coefficients in a triangle. ...

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