Zhang Qiujian

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Zhāng Qiūjiàn (張 邱建, * around 430 in China , † around 490) was a Chinese mathematician.

Nothing is known about Zhang except that he is the author of the mathematical treatise Zhang Qiujian Suanjing . It is usually dated between 468 and 486 due to a field taxation task.

The book consists of three chapters with 32, 22 and 38 problems in the individual chapters, which include the extraction of roots (square roots, cube roots) and the solution of quadratic equations, the solution of systems of linear equations, series summation and fractions (with determination of the greatest common divisor, what is called difficult in the book) to geometry (calculation of volumes and areas). In some places, the use of slide rules and tables is explicitly discussed. There is also criticism of older authors (Xiahou Yang).

Of particular interest to later Chinese authors was the “problem of the hundred birds”, which from today's perspective simply leads to the solution (in natural numbers) of two linear equations in three unknowns, with four possible solutions (of which the Chinese only three interested, which were given as a solution in the book). Such tasks were found difficult by the Chinese for a long time afterwards.

The book is similar to the book Nine Books of Arithmetic Technique ( Jiu Zhang Suanshu ) , which is mostly dated to the first or second century BC, and takes this as a model, but mathematically goes beyond it.

The book was edited (656) by Li Chunfeng (602–670) textbook for the Imperial State Examinations for Civil Servants, as one of the "Ten Mathematical Classics" ( Suanjing shi shu ) in China. The oldest (incomplete) surviving edition is a South Song print from 1213 in the Shanghai library and contains Li’s commentary.

literature

  • Ang Tian Se: A study of the mathematical manual of Chang Ch'iu-Chien , 1969 (Master's thesis / diploma thesis with Lam Lay Yong , National University of Singapore)
  • Jean-Claude Martzloff : A history of Chinese mathematics , Springer, 1997, ISBN 3-540-54749-5 (English translation of Histoire des mathématiques chinoises , 1988, from the French by Stephen S. Wilson; doi : 10.1007 / 978-3 -540-33783-6 , Zentralblatt review )
  • Lam Lay Yong : Zhang Qiujian suanjing (The mathematical classic of Zhang Qiujian): an overview , Archive for History of Exact Sciences 50, 1997, pp. 201–240 (English; Zentralblatt review )
  • Andrea Bréard: Re-creation of a mathematical concept in the Chinese discourse. "Series" from the 1st to the 19th century , Franz Steiner, Stuttgart 1999, ISBN 3-515-07451-1 (Dissertation TU Berlin 1997; Zentralblatt review ; review , PDF file, 5.4 MB)
  • Joseph W. Dauben : Chinese Mathematics , Chapter 3 in Victor J. Katz (Ed.): The mathematics of Egypt, Mesopotamia, China, India and Islam. A sourcebook , Princeton University Press, 2007, ISBN 978-0-691-11485-9 , pp. 187–384 (English; with partial reprint in English translation on pp. 304–307)

Web links

Individual evidence

  1. ↑ Qian Baocong : Ten Mathematical Classics , Beijing 1963 (Chinese), which also includes Zhang Qiujian's book. Problem 13 of Chapter 2 mentions a tax system that only existed for a short time in the Northern Wei Dynasty.
  2. ↑ In the oldest surviving edition, only 15 of Chapter 1 have survived. Ho-Peng Yoke (1965) and others reconstructed the missing tasks from other sources.
  3. ↑ A rooster costs five copper coins (quian), a hen three and three chicks cost one copper coin. 100 birds are bought for 100 copper coins. How many of each variety are there?
  4. ↑ Martzloff, p. 308
personal data
SURNAME Zhang, Qiujian
ALTERNATIVE NAMES Zhāng, Qiūjiān; 張 邱建
BRIEF DESCRIPTION Chinese mathematician
DATE OF BIRTH at 430
PLACE OF BIRTH China
DATE OF DEATH at 490