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Zhoubi Suanjing

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Zhoubi Suanjing
The Gougu Theorem diagram added to the Zhoubi by Zhao Shuang
Zhoubi Suanjing
Traditional ChineseChuBễTínhKinh
Simplified ChineseChuBễTínhKinh
Zhoubi
ChineseChuBễ
Literal meaning
  • The Zhougnomon
  • On gnomons and circular paths
Zhoubi
Traditional ChineseTínhKinh
Simplified ChineseTínhKinh
Literal meaning
  • Classic of computation
  • Arithmetic classic

TheZhoubi Suanjing,also known bymany other names,is an ancient Chinese astronomical and mathematical work. TheZhoubiis most famous for its presentation ofChinese cosmologyand a form of thePythagorean theorem.It claims to present 246 problems worked out by theDuke of Zhouas well as members of his court, placing its composition during the 11th century BC. However, the present form of the book does not seem to be earlier than theEastern Han(25–220 AD), with some additions and commentaries continuing to be added for several more centuries.

Names[edit]

The work's original title was simply theZhoubi:the characterBễis a literary term for thefemurorthighbonebut in context only refers to one or moregnomons,large sticks whose shadows were used forChinese calendricalandastronomical calculations.[1]Because of the ambiguous nature of the characterChu,it has been alternately understood and translated as 'On the gnomon and the circular paths ofHeaven',[1]the 'Zhou shadow gauge manual',[2]the 'Gnomon of the Zhou sundial',[3]and 'Gnomon of theZhou dynasty'.[4]The honorificSuanjing—'Arithmetical classic',[5]'Sacred book of arithmetic',[6]'Mathematical canon',[4]'Classic of computations',[7]—was added later.

Dating[edit]

Examples of thegnomondescribed in the work have been found from as early as 2300 BC and theDuke of Zhou,was an 11th-century BC regent and noble during the first generation of theZhou dynasty.TheZhoubiwas traditionally dated to the Duke of Zhou's own life[8]and considered to be the oldest Chinese mathematical treatise.[1]However, although some passages seem to come from theWarring States periodor earlier,[8]the current text of the work mentionsLü Buweiand is believed to have received its current form no earlier than theEastern Han,during the 1st or 2nd century. The earliest known mention of the text is from a memorial dedicated to the astronomerCai Yongin 178 AD.[9]It does not appear at all in theBook of Han's account of calendrical, astronomical, and mathematical works, althoughJoseph Needhamallows that this may have been from its current contents having previously been provided in several different works listed in the Han history which are otherwise unknown.[1]

Contents[edit]

A umbrella-coveredchariotfrom theterracotta armyof thetomb of Qin Shi Huang(2006)

TheZhoubiis an anonymous collection of 246 problems[dubious–discuss]encountered by the Duke of Zhou and figures in his court, including theastrologerShang Gao. Each problem includes an answer and a corresponding arithmeticalgorithm.

It is an important source on earlyChinese cosmology,glossing the ancient idea of a round heaven over a square earth (ThiênViênMàPhương,tiānyuán dìfāng) as similar to the round parasol suspended over some ancientChinese chariots[10]or aChinese chessboard.[11]All things measurable were considered variants of thesquare,while the expansion of a polygon to infinite sides approaches the immeasurablecircle.[2]This concept of a 'canopy heaven' (CáiThiên,gàitiān) had earlier produced the jadebi(Bích) andcongobjects andmythsaboutGonggong,Mount Buzhou,Nüwa,andrepairing the sky.Although this eventually developed into an idea of a 'spherical heaven' (HồnThiên,hùntiān),[12]theZhoubioffers numerous explorations of the geometric relationships of simple circlescircumscribed by squaresand squarescircumscribed by circles.[13]A large part of this involves analysis ofsolar declinationin the Northern Hemisphere at various points throughout the year.[1]

At one point during its discussion of the shadows cast by gnomons, the work presents a form of thePythagorean theoremknown as thegougu theorem(Định lý PythagorasĐịnh lý)[14]from the Chinese names—lit. 'hook' and 'thigh'—of the two sides of thecarpenterortry square.[15]In the 3rd century, Zhao Shuang's commentary on theZhoubiincluded a diagram effectively proving the theorem[16]for the case of a3-4-5 triangle,[17]whence it can be generalized to allright triangles.The original text being ambiguous on its own, there is disagreement as to whether this proof was established by Zhao or merely represented an illustration of a previously understood concept earlier thanPythagoras.[18][14]Shang Gao concludes the gougu problem saying "He who understands the earth is a wise man, and he who understands the heavens is a sage. Knowledge is derived from the shadow [straight line], and the shadow is derived from the gnomon [right angle]. The combination of the gnomon with numbers is what guides and rules the ten thousand things."[19]

Commentaries[edit]

TheZhoubihas had a prominent place inChinese mathematicsand was the subject of specific commentaries by Zhao Shuang in the 3rd century,Liu Huiin 263, byZu Gengzhiin the early 6th century,Li Chunfengin the 7th century, andYang Huiin 1270.

Translation[edit]

A translation to English was published in 1996 by Christopher Cullen, through the Cambridge University Press, entitledAstronomy and mathematics in ancient China: the Zhou bi suan jing.[20]The work includes a preface attributed to Zhao Shuang, as well as his discussions and diagrams for the gougu theorem, the height of the sun, the sevenhengand his gnomon shadow table, restored.

See also[edit]

References[edit]

Citations[edit]

  1. ^abcdeNeedham & al. (1959),p.19.
  2. ^abZou (2011),p.104.
  3. ^Pang-White (2018),p.464.
  4. ^abCullen (2018),p.758.
  5. ^Needham & al. (1959),p.815.
  6. ^Davis & al. (1995),p.28.
  7. ^Elman (2015),p.240.
  8. ^abNeedham & al. (1959),p.20.
  9. ^Patrick Morgan, Daniel (2 November 2018)."A Radical Proposition on the Origins of the Received Mathematical Classic The Gnomon of Zhou (Zhoubi chu bễ )".The Second International Conference on History of Mathematics and Astronomy:4.Retrieved25 December2023.
  10. ^Tseng (2011),pp. 45–49.
  11. ^Ding (2020),p.172.
  12. ^Tseng (2011),p. 50.
  13. ^Tseng (2011),p. 51.
  14. ^abCullen (1996),p. 82.
  15. ^Gamwell (2016),p.39.
  16. ^Cullen (1996),p. 208.
  17. ^Chemla (2005),p.[page needed].
  18. ^Chemla (2005).
  19. ^Gamwell (2016),p.41.
  20. ^Cullen, Christopher (1996).Astronomy and mathematics in ancient China: the Zhou bi suan jing.Needham Research Institute studies. Cambridge University Press.ISBN978-0-521-55089-5.

Works cited[edit]

Further reading[edit]

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