# rod numerals

Yang Hui (Pascal's) triangle, as depicted by Zhu Shijie in 1303, using rod numerals.

Counting rods (Traditional Chinese: ; Simplified Chinese: ; 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.

rod number 231
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).

For a look of the ancient counting rods, and further explanation, you can visit the sites:
Child systems Simplified Chinese
Chữ NÃ´m
Sister systems Hanja, Kanji

ISO 15924 Hant

Simplified Chinese

Sister systems Kanji, Chữ NÃ´m

ISO 15924 Hans

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Pinyin, more formally called Hanyu Pinyin (Simplified Chinese: 汉语拼音; Traditional Chinese: 漢語拼音
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Shang Dynasty (Chinese: ) or Yin Dynasty () (ca. 1750 BC - ca. 1045 BC) is the second historic Chinese dynasty and ruled in the northeastern region of the area known as "China proper", in the Yellow River valley.
History of China
ANCIENT
3 Sovereigns and 5 Emperors
Xia Dynasty 2070–1600 BCE
Shang Dynasty 1600–1046 BCE
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Rod calculus or rod calculation is the method of mathematical computation with counting rods in China from The Warring States to Ming dynasty before the counting rods were replaced by more convenient and faster abacus.

An abacus (plurals abacuses or abaci), also called a counting frame, is a calculating tool for performing arithmetical processes, often constructed as a wooden frame with beads
A negative number is a number that is less than zero, such as −3. A positive number is a number that is greater than zero, such as 3. Zero itself is neither positive nor negative.
A negative number is a number that is less than zero, such as −3. A positive number is a number that is greater than zero, such as 3. Zero itself is neither positive nor negative.
Rod calculus or rod calculation is the method of mathematical computation with counting rods in China from The Warring States to Ming dynasty before the counting rods were replaced by more convenient and faster abacus.
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In mathematics, a square root of a number x is a number r such that , or in words, a number r whose square (the result of multiplying the number by itself) is x.
cube root of a number, denoted or x1/3, is a number a such that a3 = x. All real numbers have exactly one real cube root and 2 complex roots, and all nonzero complex numbers have 3 distinct complex cube roots.
In mathematics, an nth root of a number a is a number b such that bn=a. When referring to the nth root of a real number a it is assumed that what is desired is the principal nth root
system of linear equations (or linear system) is a collection of linear equations involving the same set of variables. For example,
is a system of three equations in the three variables .
Operations Research or Operational Research (OR) is an interdisciplinary branch of mathematics which uses methods like mathematical modeling, statistics, and algorithms to arrive at optimal or good decisions in complex problems which are concerned with optimizing the maxima
0 (zero) is both a number and a numerical digit used to represent that number in numerals. It plays a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures.
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Numeral systems by culture
Hindu-Arabic numerals
Western Arabic
Eastern Arabic
Khmer Indian family