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藝游錄

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Text ID
KR3fc080
Date
1800–1841
Dynasty
清

Yìyóu lù 藝游錄

Record of My Wanderings in the [Mathematical] Arts by 駱騰鳳 (撰)

About the work

駱騰鳳 Luò Téngfèng’s (1770–1841) collected mathematical writings, published posthumously in Guāngxù 10 (1884) by his descendants. The collection covers Luò’s principal mathematical contributions in the indigenous Chinese mathematical tradition: the qiúyī shù 求一術 (Chinese Remainder Theorem), the tiānyuán 天元 algebraic apparatus, and various indigenous procedural-arithmetical methods. (The catalog meta’s extent field gives “1884” — the publication date rather than a juan-count or a date-range. The work as transmitted is generally cited as a single composite collection without a fixed juàn enumeration.)

Abstract

The Yìyóu lù (literally “record of [my] wanderings in the [mathematical] arts” — yìyóu 藝游 evoking both “playful study” and “wandering through the [mathematical] arts”) is the principal monument of 駱騰鳳 Luò Téngfèng’s substantial but locally-circulated mathematical work. The collection’s title and the posthumous publication some four decades after Luò’s death (1841 death, 1884 publication, by his descendants) reflect the marginal status of Luò’s mathematical work during his lifetime — he was a provincial jǔrén without significant official career, working largely outside the metropolitan mathematical circles.

The collection’s principal mathematical contributions:

(1) The qiúyī shù tradition. Luò’s contribution to the indigenous Chinese form of the Chinese Remainder Theorem is the most substantial part of the collection. He extends 秦九韶 Qín Jiǔsháo’s procedure (in Shùshū jiǔzhāng Chapter 1, KR3fc008) to cover cases with non-coprime moduli — the cases that 羅士琳 Luó Shìlín had identified as algorithmically problematic. Luò Téngfèng’s treatment is one of the principal nineteenth-century mathematical contributions to the qiúyī tradition, alongside the works of 時曰醇 Shí Yuēchún and 黃遵憲 Huáng Zūnxiàn (KR3fc079).

(2) The tiānyuán apparatus. Luò’s work on the indigenous tiānyuán “celestial element” algebraic notation extends the recovery-and-systematisation project initiated by 李銳 Lǐ Ruì and 汪萊 Wāng Lái. He works through a substantial set of standard tiānyuán problem-types with detailed procedural commentary.

(3) Miscellaneous indigenous procedures. The collection also covers various computational-arithmetical procedures including continued fractions, indeterminate equations, and the procedural arithmetic of fractions and surds.

The work is one of the principal documentary sources for early-nineteenth-century provincial indigenous Chinese mathematics — the mathematical activity that took place outside the patronage circles centred on 阮元 Ruǎn Yuán (Yángzhōu / Sūzhōu), 李兆洛 Lǐ Zhàoluò (Chángzhōu), and 項名達 Xiàng Míngdá (Hángzhōu).

Dating: Luò Téngfèng lived 1770–1841; composition spans his mature productive period. notBefore 1800; notAfter 1841 (death year). Published 1884. Catalog meta gives extent “1884” which is the publication date — the dating bracket is for composition, not publication.

Translations and research

  • Libbrecht, Ulrich. 1973. Chinese Mathematics in the Thirteenth Century: the Shu-shu chiu-chang of Ch’in Chiu-shao. Cambridge, Mass.: MIT Press. — Discusses Luò Téngfèng’s contribution to the qiú-yī tradition.
  • Wú Wénjùn 吳文俊, ed. 1985. Zhōng-guó shù-xué shǐ dà-xì 中國數學史大系, vol. 7–8.
  • Tián Miǎo 田淼. 2003. Zhōng-guó shù-xué de xī-huà lì-chéng 中國數學的西化歷程.

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