Suàn shù shu
Encyclopedia
The Suàn shù shū or the Writings on Reckoning (also as Book on Numbers and Computation), is one of the earliest known Chinese mathematical treatises
. It was written during the early Western Han Dynasty
, sometime between 202 BC
and 186 BC
.
, Jiangling County, in Hubei
province, excavated in December–January 1983–1984. This tomb belonged to an anonymous civil servant in early West Han dynasty. In the tomb were 1200 bamboo strips written in ink. Originally the strips were bound together with string, but the string had rotted away and it took Chinese scholars 17 years to piece together the strips. As well as the mathematical work the strips covered government statutes, law reports and therapeutic gymnastics.
On the back of #6 strip, the top has a black square mark,followed by three characthers 筭數書, which served as title of the rolled up book.
written in ink, 180 strips are intact, the others have rotted. They consist of 69 mathematical problems from a variety of sources, two names Mr Wáng and Mr Yáng were found, probably two of the writers. Each problem has a question, an answer, followed by a method. The problems cover elementary arithmetic
; fractions
;inverse proportion; factorization of number; geometric progression
s, in particular interest rate
calculations and handling of errors; conversion between different units; the false position method
for finding roots and the extraction of approximate square root
s; calculation of the volume
of various 3-dimensional shapes; relative dimensions of a square
and its inscribed circle
; Calculation of unknown side of rectangle, given area and one side. All the calculations about circumference and area of circle are approximate, equivalent to taking π = 3. Calculations of pi were made more accurate with the work of Liu Xin
(c. 46 BC – 23 AD), Zhang Heng
(78–139 AD), Liu Hui
(fl. 3rd century AD), and Zu Chongzhi
(429–500).
Prior to discovery the oldest Chinese mathematical text were the Chou Pei Suan Ching
and the The Nine Chapters on the Mathematical Art
which dates from around 100 CE. Many topics are covered in both texts, however, error correction problems only appear in the Suàn shù shū, and the last two chapter of the nine chapters have no corresponding material in the Suàn shù shū.
The text has been translated to English by Christopher Cullen director of the Needham Research Institute
.
Chinese mathematics
Mathematics in China emerged independently by the 11th century BC. The Chinese independently developed very large and negative numbers, decimals, a place value decimal system, a binary system, algebra, geometry, and trigonometry....
. It was written during the early Western Han Dynasty
Han Dynasty
The Han Dynasty was the second imperial dynasty of China, preceded by the Qin Dynasty and succeeded by the Three Kingdoms . It was founded by the rebel leader Liu Bang, known posthumously as Emperor Gaozu of Han. It was briefly interrupted by the Xin Dynasty of the former regent Wang Mang...
, sometime between 202 BC
202 BC
Year 202 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Geminus and Nero...
and 186 BC
186 BC
Year 186 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Albinus and Philippus...
.
Discovery
The text was found in tomb M247 of the burial grounds near ZhangjiashanZhangjiashan Han bamboo texts
The Zhangjiashan Han bamboo texts are ancient Han Dynasty Chinese written works dated 196–186 BCE. They were discovered in 1983 by archaeologists excavating tomb no. 247 at Mount Zhangjia of Jiangling County, Hubei Province . The tomb was built for an early Western Han era official who had...
, Jiangling County, in Hubei
Hubei
' Hupeh) is a province in Central China. The name of the province means "north of the lake", referring to its position north of Lake Dongting...
province, excavated in December–January 1983–1984. This tomb belonged to an anonymous civil servant in early West Han dynasty. In the tomb were 1200 bamboo strips written in ink. Originally the strips were bound together with string, but the string had rotted away and it took Chinese scholars 17 years to piece together the strips. As well as the mathematical work the strips covered government statutes, law reports and therapeutic gymnastics.
On the back of #6 strip, the top has a black square mark,followed by three characthers 筭數書, which served as title of the rolled up book.
Content
The Suàn shù shū consists of 200 strips of bambooBamboo
Bamboo is a group of perennial evergreens in the true grass family Poaceae, subfamily Bambusoideae, tribe Bambuseae. Giant bamboos are the largest members of the grass family....
written in ink, 180 strips are intact, the others have rotted. They consist of 69 mathematical problems from a variety of sources, two names Mr Wáng and Mr Yáng were found, probably two of the writers. Each problem has a question, an answer, followed by a method. The problems cover elementary arithmetic
Elementary arithmetic
Elementary arithmetic is the simplified portion of arithmetic which is considered necessary and appropriate during primary education. It includes the operations of addition, subtraction, multiplication, and division. It is taught in elementary school....
; fractions
Fraction (mathematics)
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, we specify how many parts of a certain size there are, for example, one-half, five-eighths and three-quarters.A common or "vulgar" fraction, such as 1/2, 5/8, 3/4, etc., consists...
;inverse proportion; factorization of number; geometric progression
Geometric progression
In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression...
s, in particular interest rate
Interest rate
An interest rate is the rate at which interest is paid by a borrower for the use of money that they borrow from a lender. For example, a small company borrows capital from a bank to buy new assets for their business, and in return the lender receives interest at a predetermined interest rate for...
calculations and handling of errors; conversion between different units; the false position method
False position method
The false position method or regula falsi method is a term for problem-solving methods in algebra and calculus. In simple terms, these methods begin by attempting to evaluate a problem using test values for the variables, and then adjust the values accordingly.-Algebra:In algebra, the false...
for finding roots and the extraction of approximate square root
Square root
In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...
s; calculation of the volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....
of various 3-dimensional shapes; relative dimensions of a square
Square (geometry)
In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles...
and its inscribed circle
Circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
; Calculation of unknown side of rectangle, given area and one side. All the calculations about circumference and area of circle are approximate, equivalent to taking π = 3. Calculations of pi were made more accurate with the work of Liu Xin
Liu Xin
Liu Xin , later changed name to Liu Xiu , courtesy name Zijun , was a Chinese astronomer, historian, and editor during the Xin Dynasty . He was the son of Confucian scholar Liu Xiang and an associate of other prominent thinkers such as the philosopher Huan Tan...
(c. 46 BC – 23 AD), Zhang Heng
Zhang Heng
Zhang Heng was a Chinese astronomer, mathematician, inventor, geographer, cartographer, artist, poet, statesman, and literary scholar from Nanyang, Henan. He lived during the Eastern Han Dynasty of China. He was educated in the capital cities of Luoyang and Chang'an, and began his career as a...
(78–139 AD), Liu Hui
Liu Hui
Liu Hui was a mathematician of the state of Cao Wei during the Three Kingdoms period of Chinese history. In 263, he edited and published a book with solutions to mathematical problems presented in the famous Chinese book of mathematic known as The Nine Chapters on the Mathematical Art .He was a...
(fl. 3rd century AD), and Zu Chongzhi
Zu Chongzhi
Zu Chongzhi , courtesy name Wenyuan , was a prominent Chinese mathematician and astronomer during the Liu Song and Southern Qi Dynasties.-Life and works:...
(429–500).
Prior to discovery the oldest Chinese mathematical text were the Chou Pei Suan Ching
Chou Pei Suan Ching
The Zhou Bi Suan Jing, or Chou Pei Suan Ching, is one of the oldest and most famous Chinese mathematical texts. The title literally means The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven....
and the The Nine Chapters on the Mathematical Art
The Nine Chapters on the Mathematical Art
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...
which dates from around 100 CE. Many topics are covered in both texts, however, error correction problems only appear in the Suàn shù shū, and the last two chapter of the nine chapters have no corresponding material in the Suàn shù shū.
The text has been translated to English by Christopher Cullen director of the Needham Research Institute
Needham Research Institute
The Needham Research Institute or NRI, located on the grounds of the Robinson College, in Cambridge, England, is a center for research into the history of science, technology and medicine in East Asia. It is part of the University of Cambridge...
.
External links
- Full text of book Christopher Cullen: Suan shu shu Writings on reckoning Needham Research InstituteNeedham Research InstituteThe Needham Research Institute or NRI, located on the grounds of the Robinson College, in Cambridge, England, is a center for research into the history of science, technology and medicine in East Asia. It is part of the University of Cambridge...