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Counting rods
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Small bars used for calculating in ancient East Asia
Counting rodsChinese nameTraditional Chinese算籌Simplified Chinese算筹TranscriptionsStandard MandarinHanyu PinyinsuànchóuIPAsu̯än⁵¹ ʈ͡ʂʰoʊ̯³⁵Alternative Chinese nameChinese算子TranscriptionsStandard MandarinHanyu PinyinsuànzǐIPAsu̯än⁵¹ t͡sz̩²¹⁴⁻²¹⁽⁴⁾Vietnamese nameVietnamese alphabetque tính / toán trùHán-Nôm𣠗併 / 算籌Korean nameHangul산가지 / 산목Hanja算가지 / 算木TranscriptionsRevised Romanizationsangaji / sanmokJapanese nameKanji算木 / 算籌Hiraganaさんぎ / さんちゅうTranscriptionsRomanizationsangi / sanchū
Yang Hui (Pascal's) triangle, as depicted by Zhu Shijie in 1303, using rod numeralsCounting rods (筭) are small bars, typically 3–14 cm (1" to 6") long, that were used by mathematicians for calculation in ancient East Asia. They are placed either horizontally or vertically to represent any integer or rational number.
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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)[1] to the 16th century.
History<br>[edit]
Chinese arithmeticians used counting rods for well over two thousand years ago.
In 1954, forty-odd counting rods of the Warring States period (5th century BCE to 221 BCE) were found in Zuǒjiāgōngshān (左家公山) Chu Grave No.15 in Changsha, Hunan.[2][3][failed verification]
In 1973, archeologists unearthed a number of wood scripts from a tomb in Hubei dating from the period of the Han dynasty (206 BCE to 220 CE). On one of the wooden scripts was written: "当利二月定算𝍥".[citation needed] This is one of the earliest examples of using counting-rod numerals in writing.
A square lacquer box, dating from c. 168 BCE, containing a square chess board with the TLV patterns, chessmen, counting rods, and other items, was excavated in 1972, from Mawangdui M3, Changsha, Hunan Province.[4][5]
In 1976, a bundle of Western Han-era (202 BCE to 9 CE) counting rods made of bones was unearthed from Qianyang County in Shaanxi.[6][7] The use of counting rods must predate it; Sunzi (c. 544 to c. 496 BCE), a military strategist at the end of Spring and Autumn period of 771 BCE to 5th century BCE, mentions their use to make calculations to win wars before going into the battle;[8] Laozi (died 531 BCE), writing in the Warring States period, said "a good calculator doesn't use counting rods".[9] The Book of Han (finished 111 CE) recorded: "they calculate with bamboo, diameter one fen, length six cun, arranged into a hexagonal bundle of two hundred seventy one pieces".[10]
At first, calculating rods were round in cross-section, but by the time of the Sui dynasty (581 to 618 CE) mathematicians used triangular rods to represent positive numbers and rectangular rods for negative numbers.[citation needed]
Toán trù 算籌 (counting rods) in a Vietnamese mathematics textbook, Cửu chương lập thành toán pháp 九章立成算法 is shown at the bottom of the page.<br>After the abacus flourished[when?], counting rods were abandoned except in Japan, where rod numerals developed into a symbolic notation for algebra.
Usage<br>[edit]
Rod numeral place value from Yongle Encyclopedia: 71,824<br>Japanese counting board with grids<br>A checker counting board diagram in an 18th-century Japanese mathematics textbook<br>Counting rod numerals in grids in a Japanese mathematic book<br>Counting rods represent digits by the number of rods, and the perpendicular rod represents five. To avoid confusion, vertical and horizontal forms are alternately used. Generally, vertical rod numbers...