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Zhoubi Suanjing | |||||||||
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Zhoubi Suanjing | |||||||||
Traditional Chinese | 周 髀 算 經 | ||||||||
Simplified Chinese | 周 髀 算 经 | ||||||||
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Zhoubi | |||||||||
Chinese | 周 髀 | ||||||||
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Suanjing | |||||||||
Traditional Chinese | 算 經 | ||||||||
Simplified Chinese | 算 经 | ||||||||
Literal meaning |
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The Zhoubi Suanjing, also known by many other names,is an ancient Chinese astronomical and mathematical work. The Zhoubi is most famous for its presentation of Chinese cosmology and a form of the Pythagorean theorem. It claims to present 246 problems worked out by the Duke of Zhou as 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 the Eastern Han (25–220 AD),with some additions and commentaries continuing to be added for several more centuries.
The book was included as part of the Ten Computational Canons .
The work's original title was simply the Zhoubi:the character 髀 is a literary term for the femur or thighbone but in context only refers to one or more gnomons,large sticks whose shadows were used for Chinese calendrical and astronomical calculations. [1] Because of the ambiguous nature of the character 周 ,it has been alternately understood and translated as 'On the gnomon and the circular paths of Heaven', [1] the 'Zhou shadow gauge manual', [2] the 'Gnomon of the Zhou sundial', [3] and 'Gnomon of the Zhou dynasty'. [4] The honorific Suanjing—'Arithmetical classic', [5] 'Sacred book of arithmetic', [6] 'Mathematical canon', [4] 'Classic of computations', [7] —was added later.
Examples of the gnomon described in the work have been found from as early as 2300 BC and the Duke of Zhou,was an 11th-century BC regent and noble during the first generation of the Zhou dynasty. The Zhoubi was 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 the Warring States period or earlier, [8] the current text of the work mentions LüBuwei and is believed to have received its current form no earlier than the Eastern Han,during the 1st or 2nd century. The earliest known mention of the text is from a memorial dedicated to the astronomer Cai Yong in 178 AD. [9] It does not appear at all in the Book of Han's account of calendrical,astronomical,and mathematical works,although Joseph Needham allows 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]
The Zhoubi is an anonymous collection of 246 problems[ dubious – discuss ] encountered by the Duke of Zhou and figures in his court,including the astrologer Shang Gao. Each problem includes an answer and a corresponding arithmetic algorithm.
It is an important source on early Chinese cosmology,glossing the ancient idea of a round heaven over a square earth ( 天 圆 地 方 ,tiānyuán dìfāng) as similar to the round parasol suspended over some ancient Chinese chariots [10] or a Chinese chessboard. [11] All things measurable were considered variants of the square,while the expansion of a polygon to infinite sides approaches the immeasurable circle. [2] This concept of a 'canopy heaven' ( 蓋 天 ,gàitiān) had earlier produced the jade bi ( 璧 ) and cong objects and myths about Gonggong,Mount Buzhou,Nüwa,and repairing the sky. Although this eventually developed into an idea of a 'spherical heaven' ( 渾 天 ,hùntiān), [12] the Zhoubi offers numerous explorations of the geometric relationships of simple circles circumscribed by squares and squares circumscribed by circles. [13] A large part of this involves analysis of solar declination in 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 the Pythagorean theorem known as the gougu theorem ( 勾股 定理 ) [14] from the Chinese names—lit. 'hook' and 'thigh'—of the two sides of the carpenter or try square. [15] In the 3rd century,Zhao Shuang's commentary on the Zhoubi included a diagram effectively proving the theorem [16] for the case of a 3-4-5 triangle, [17] whence it can be generalized to all right 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 than Pythagoras. [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]
The Zhoubi has had a prominent place in Chinese mathematics and was the subject of specific commentaries by Zhao Shuang in the 3rd century,Liu Hui in 263,by Zu Gengzhi in the early 6th century,Li Chunfeng in the 7th century,and Yang Hui in 1270.
A translation to English was published in 1996 by Christopher Cullen,through the Cambridge University Press,entitled Astronomy 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 seven heng and his gnomon shadow table,restored.
Flat Earth is an archaic and scientifically disproven conception of the Earth's shape as a plane or disk. Many ancient cultures subscribed to a flat-Earth cosmography,notably including ancient near eastern cosmology. The model has undergone a recent resurgence as a conspiracy theory.
The Zhou dynasty was a royal dynasty of China that existed for 789 years from c. 1046 BC until 256 BC,the longest of all dynasties in Chinese history. During the Western Zhou period,the royal house,surnamed Ji,had military control over ancient China. Even as Zhou suzerainty became increasingly ceremonial over the following Eastern Zhou period (771–256 BC),the political system created by the Zhou royal house survived in some form for several additional centuries. A date of 1046 BC for the Zhou's establishment is supported by the Xia–Shang–Zhou Chronology Project and David Pankenier,but David Nivison and Edward L. Shaughnessy date the establishment to 1045 BC.
A gnomon is the part of a sundial that casts a shadow. The term is used for a variety of purposes in mathematics and other fields.
Luoyang is a city located in the confluence area of the Luo River and the Yellow River in the west of Henan province,China. Governed as a prefecture-level city,it borders the provincial capital of Zhengzhou to the east,Pingdingshan to the southeast,Nanyang to the south,Sanmenxia to the west,Jiyuan to the north,and Jiaozuo to the northeast. As of December 31,2018,Luoyang had a population of 6,888,500 inhabitants with 2,751,400 people living in the built-up area made of the city's five out of six urban districts and Yanshi District,now being conurbated. By the end of 2022,Luoyang Municipality had jurisdiction over 7 municipal districts,7 counties and 1 development zone. The permanent population is 7.079 million.
An armillary sphere is a model of objects in the sky,consisting of a spherical framework of rings,centered on Earth or the Sun,that represent lines of celestial longitude and latitude and other astronomically important features,such as the ecliptic. As such,it differs from a celestial globe,which is a smooth sphere whose principal purpose is to map the constellations. It was invented separately,in ancient China possibly as early as the 4th century BC and ancient Greece during the 3rd century BC,with later uses in the Islamic world and Medieval Europe.
Liu Hui was a Chinese mathematician who published a commentary in 263 CE on Jiu Zhang Suan Shu. He was a descendant of the Marquis of Zixiang of the Eastern Han dynasty and lived in the state of Cao Wei during the Three Kingdoms period of China.
The Nine Chapters on the Mathematical Art is a Chinese mathematics book,composed by several generations of scholars from the 10th–2nd century BCE,its latest stage being from the 1st century CE. This book is one of the earliest surviving mathematical texts from China,the others being the Suan shu shu and Zhoubi Suanjing. It lays out an approach to mathematics that centres on finding the most general methods of solving problems,which may be contrasted with the approach common to ancient Greek mathematicians,who tended to deduce propositions from an initial set of axioms.
King Zhao of Zhou,personal name Ji Xia,was the fourth king of the Zhou dynasty of China. He ruled from 977/75 BC until his death twenty years later. Famous for his disastrous war against the Chu confederation,his death in battle ended the Western Zhou's early expansion and marked the beginning of his dynasty's decline.
King Mu of Zhou,personal name Ji Man,was the fifth king of the Zhou dynasty of China. The dates of his reign are 976–922 BC or 956–918 BC.
Liu Xin,courtesy name Zijun,was a Chinese astronomer,classicist,librarian,mathematician,and politician during the Western Han and Xin dynasties. He later changed his name to Liu Xiu (劉秀) due to the naming taboo of Emperor Ai of Han. He was the son of Imperial librarian Liu Xiang and an associate of other eminent thinkers such as the philosopher Huan Tan. Liu was a prominent supporter of the Old Text classics.
Astronomy in China has a long history stretching from the Shang dynasty,being refined over a period of more than 3,000 years. The ancient Chinese people have identified stars from 1300 BCE,as Chinese star names later categorized in the twenty-eight mansions have been found on oracle bones unearthed at Anyang,dating back to the mid-Shang dynasty. The core of the "mansion" system also took shape around this period,by the time of King Wu Ding.
Mathematics emerged independently in China by the 11th century BCE. The Chinese independently developed a real number system that includes significantly large and negative numbers,more than one numeral system,algebra,geometry,number theory and trigonometry.
Science in the ancient world encompasses the earliest history of science from the protoscience of prehistory and ancient history to late antiquity. In ancient times,culture and knowledge were passed through oral tradition. The development of writing further enabled the preservation of knowledge and culture,allowing information to spread accurately.
Pei Xiu (224–271),courtesy name Jiyan,was a Chinese cartographer,geographer,politician,and writer of the state of Cao Wei during the late Three Kingdoms period and Jin dynasty of China. He was very much trusted by Sima Zhao,and participated in the suppression of Zhuge Dan's rebellion. Following Sima Yan taking the throne of the newly established Jin dynasty,he and Jia Chong had Cao Huan deprived of his position to accord to the will of heaven. In the year 267,Pei Xiu was appointed as the Minister of Works in the Jin government.
Early study of triangles can be traced to the 2nd millennium BC,in Egyptian mathematics and Babylonian mathematics. Trigonometry was also prevalent in Kushite mathematics. Systematic study of trigonometric functions began in Hellenistic mathematics,reaching India as part of Hellenistic astronomy. In Indian astronomy,the study of trigonometric functions flourished in the Gupta period,especially due to Aryabhata,who discovered the sine function,cosine function,and versine function.
Gaocheng Astronomical Observatory,also known as the Dengfeng Observatory,is an observatory in Duke of Zhou's shrine,Gaocheng Town,near Dengfeng in Henan province,China. This site has a long tradition of astronomical observations,from the time of the Western Zhou up to the early Yuan dynasty. There is also a gnomon used for the Da Yan calendar in 729 AD and the great observatory of the Yuan dynasty. As part of the "Dengfeng Historic Monuments of Dengfeng 'in the Center of Heaven and Earth'" the observatory was listed as a UNESCO World Heritage Site in 2010.
The Han dynasty of early imperial China,divided between the eras of Western Han,the Xin dynasty of Wang Mang,and Eastern Han,witnessed some of the most significant advancements in premodern Chinese science and technology.
Li Ye,born Li Zhi,courtesy name Li Jingzhai,was a Chinese mathematician,politician,and writer who published and improved the tian yuan shu method for solving polynomial equations of one variable. Along with the 4th-century Chinese astronomer Yu Xi,Li Ye proposed the idea of a spherical Earth instead of a flat one before the advances of European science in the 17th century.
Christopher Cullen is an English sinologist born in 1946. He has an MA from University of Oxford in engineering and a PhD from the School of Oriental and African Studies in classical Chinese. He is Director Emeritus of the Needham Research Institute and General Editor of the Science and Civilisation in China series,succeeding Joseph Needham. His own area of research is the Han Dynasty and he translated the Book on Numbers and Computation into English.
Yu Xi,courtesy name Zhongning (仲寧),was a Chinese astronomer,politician,and writer of the Jin dynasty. He is best known for his discovery of the precession of the equinoxes,independently of the earlier ancient Greek astronomer Hipparchus. He also postulated that the Earth could be spherical in shape instead of being flat and square,long before the idea became widely accepted in Chinese science with the advances in circumnavigation by Europeans from the 16th-20th centuries,especially with their arrival into the capital's imperial court in the 17th century.