Counting rods

Yang Hui (Pascal's) triangle, as depicted by Zhu Shijie in 1303, using rod numerals
Counting rods
Chinese name
Traditional Chinese算籌
Simplified Chinese算筹
Transcriptions
Standard Mandarin
Hanyu Pinyinsuànchóu
IPAsu̯än⁵¹ ʈ͡ʂʰoʊ̯³⁵
Alternative Chinese name
Chinese算子
Transcriptions
Standard Mandarin
Hanyu Pinyinsuànzǐ
IPAsu̯än⁵¹ t͡sz̩²¹⁴⁻²¹⁽⁴⁾
Vietnamese name
Vietnamese alphabetque tính / toán trù
Hán-Nôm𣠗併 / 算籌
Korean name
Hangul산가지 / 산목
Hanja算가지 / 算木
Transcriptions
Revised Romanizationsangaji / sanmok
Japanese name
Kanji算木 / 算籌
Hiraganaさんぎ / さんちゅう
Transcriptions
Romanizationsangi / sanchū

Counting 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.

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.

  1. ^ Lay-Yong, Lam (1986). "The Conceptual Origins of our Numeral System and the Symbolic Form of Algebra". Archive for History of Exact Sciences. 36 (3): 183–195. ISSN 0003-9519.