Mathematics in China emerged independently by the 11th century BC [1]. The Chinese independently developed very large and negative numbers, decimals, a decimal system, a binary system, algebra, geometry and calculus.
Most scholars believe that Chinese mathematics and the mathematics of the ancient Mediterranean world had developed more or less independently up to the time when the Nine Chapters reached its final form. It is often suggested that some Chinese mathematical discoveries predate their Western counterparts. One example is the Pythagorean theorem. In Mathematics, the Pythagorean theorem ( American English) or Pythagoras' theorem ( British English) is a relation in Euclidean geometry There is some controversy regarding this issue and the precise nature of this knowledge in early China. The Chinese were one of the most advanced in dealing with mathematical computations, and created enormous numbers. Elements of "Pythagorean" science have been found, for example, in one of the oldest Classical Chinese texts (see King Wen sequence). The King Wen sequence (文王卦序 of the Yi Jing (易經 is a series of sixty-four binary figures ( Hexagrams, each composed of 6 lines either unbroken Knowledge of Pascal's triangle has also been shown to have existed in China centuries before Pascal[2], such as by Shen Kuo. Shen Kuo or Shen Kua ( (1031&ndash1095 style name Cunzhong and pseudonym Mengqi Weng, was a Polymathic Chinese
Knowledge of Chinese mathematics before 100 BC is somewhat fragmentary, and even after this date the manuscript traditions are obscure. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and The dating of the use of certain mathematical methods in Chinese history is problematic and disputed.
In early times the focus was on astronomy and perfecting the calendar and not on establishing the proof. Astronomy (from the Greek words astron (ἄστρον "star" and nomos (νόμος "law" is the scientific study The word Calendar consist of two words 1 Cal ( in Pashto means Year in Hindi and Persian is Sal- also means Year In Mathematics, a proof is a convincing demonstration (within the accepted standards of the field that some Mathematical statement is necessarily true Many works simply listed equations or gave diagrams where a proof was hinted at rather than shown. In other cases a proof was shown but it was declared to be an established method after some fashion.
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Early Chinese mathematics
Simple mathematics inscribed on tortoise shells for writing mediums date back to the Shang Dynasty (1600 BC-1050 BC). The Shang Dynasty ( Chinese: 商[[wiktionary 朝|朝]] or Yin Dynasty ( 殷[[wiktionary 代|代]] was according to traditional sources the One of the oldest surviving mathematical works is the I Ching, which greatly influenced written literature during the Zhou Dynasty (1050 BC-256 BC). The I Ching ( Wade-Giles) or “Yì Jīng” ( Pinyin) also called “Classic of Changes” or “Book of Changes” is one of the oldest of the The Zhou Dynasty ( POJ: Chiu Tiau 1122 BC to 256 BC was preceded by the Shang Dynasty and followed by the Qin Dynasty in China. Events By place Roman Republic Rome aims for a quick end to hostilities in the First Punic War and decides to invade the For mathematics, the book included a sophisticated use of hexagrams. For symbols used in the I Ching, see Hexagram (I Ching For a Jewish symbol see Star of David.
Since the Shang period, the Chinese had already fully developed a decimal system. Since early times, Chinese understood basic arithmetic (which dominated far eastern history), algebra, equations, and negative numbers. Arithmetic or arithmetics (from the Greek word αριθμός = number is the oldest and most elementary branch of mathematics used by almost everyone Algebra is a branch of Mathematics concerning the study of structure, relation, and Quantity. An equation is a mathematical statement, in symbols, that two things are exactly the same (or equivalent A negative number is a Number that is less than zero, such as −2 Although the Chinese were more focused on arithmetic and advanced algebra for astronomical uses they were also the first to develop negative numbers, algebraic geometry (only Chinese geometry) and the usage of decimals. Astronomy (from the Greek words astron (ἄστρον "star" and nomos (νόμος "law" is the scientific study Algebraic geometry is a branch of Mathematics which as the name suggests combines techniques of Abstract algebra, especially Commutative algebra, with
The oldest existent work on geometry in China comes from the philosophical Mohist canon of c. 330 BC, compiled by the followers of Mozi (470 BC-390 BC). Mozi ( Lat as Micius, ca 470 BCE&ndashca 391 BCE was a Philosopher who lived in China during the Hundred Schools of Thought Events By Place Greece Suspected of plotting to seize power in Sparta by instigating a Helot uprising Pausanias takes Events By place Roman Republic July 18 - Brennus, a chieftain of the Senones of the Adriatic coast of The Mo Jing described various aspects of many fields associated with physical science, and provided a small wealth of information on mathematics as well. It provided an 'atomic' definition of the geometric point, stating that a line is separated into parts, and the part which has no remaining parts (i. e. cannot be divided into smaller parts) and thus forms the extreme end of a line is a point. [3] Much like Euclid's first and third definitions and Plato's 'beginning of a line', the Mo Jing stated that "a point may stand at the end (of a line) or at its beginning like a head-presentation in childbirth. Euclid ( Greek:.) fl 300 BC also known as Euclid of Alexandria, is often referred to as the Father of Geometry Biography Early life Birth and family Plato was born in Athens Greece (As to its invisibility) there is nothing similar to it. "[4] Similar to the atomists of Democritus, the Mo Jing stated that a point is the smallest unit, and cannot be cut in half, since 'nothing' cannot be halved. In Natural philosophy, atomism is the theory that all the objects in the universe are composed of very small indestructible building blocks - Atoms Or stated in Democritus ( Greek:) was a pre-Socratic Greek Materialist Philosopher (born at Abdera in Thrace ca [4] It stated that two lines of equal length will always finish at the same place,[4] while providing definitions for the comparison of lengths and for parallels,[5] along with principles of space and bounded space. [6] It also described the fact that planes without the quality of thickness cannot be piled up since they cannot mutually touch. [7] The book provided definitions for circumference, diameter, and radius, along with the definition of volume. [8]
Mathematical development of the Warring States period had already arrived at the standard of understanding the concept of limit， which led to the elements of modern calculus.
The history of mathematical development lacks some evidence. There are still debates about certain mathematical classics. For example, the Zhou Bi Suan Jing dates around 1200-1000BCE, yet many scholars believed it was written between 300-250BCE. The Zhou Bi Suan Jing (周髀算经 The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven is one of the oldest and most famous Chinese The Zhou Bi Suan Jing contains an in depth proof of the Gougu Theorem (Pythagorean Theorem) but focuses more on astronomical calculations. In Mathematics, the Pythagorean theorem ( American English) or Pythagoras' theorem ( British English) is a relation in Euclidean geometry
Qin mathematics
Not much is known about Qin dynasty mathematics, or before, due to the burning of books and burying of scholars. Not to be confused with the Qing Dynasty, the last dynasty of China Burning of the books and burial of the scholars ( is a phrase that refers to a policy and a sequence of events in the Qin Dynasty of China, between the period of
Knowledge of this period must be carefully determined by their civil projects and historical evidence. The Qin dynasty created a standard system of weights. Civil projects of the Qin dynasty were incredible feats of human engineering. Emperor Qin Shihuang ordered many men to build large, lifesize statues for the palace, tomb along with various other temples and shrines. Qin Shi Huang ( (259 BC – September 10 210 BC personal name Yíng Zhèng, was king of the Chinese State of Qin from 247 BCE to 221 BCE (during the The shape of the tomb is designed with geometric skills of architecture. It is certain that one of the greatest feats of human history; the great wall required many mathematical "techniques. " All Qin dynasty buildings and grand projects used advanced computation formulas for volume, area and proportion.
Han mathematics
In the Han Dynasty, numbers were developed into a system and used on a counting board and a set of counting rods called chousuan. Counting rods ( Japanese: 算木 sangi are small bars typically 3-14 cm long used by mathematicians for calculation in China, Japan Rod calculus or rod calculation is the method of mathematical computation with Counting rods in China from The Warring States to Ming dynasty before the The mathematicians Liu Xin (d. Liu Xin ( (ca 46 BC &ndash AD 23 later changed name to Liu Xiu (劉秀 Courtesy name Zijun (子駿 was a Chinese Astronomer 23) and Zhang Heng (78–139) gave more accurate approximations for pi than Chinese of previous centuries had used. Zhang Heng ( (CE 78–139 was an astronomer, mathematician, inventor, geographer, cartographer, artist, poet IMPORTANT NOTICE Please note that Wikipedia is not a database to store the millions of digits of π please refrain from adding those to Wikipedia as it could cause technical problems Zhang also applied mathematics in his work in astronomy. Astronomy in China has a very long history Oracle bones from the Shang Dynasty ( 2nd millennium BC) record eclipses and novae
The Nine Chapters on the Mathematical Art (九章算術) is a Chinese mathematics book, its oldest archeological date being 179 AD (traditionally dated 1000BC), but perhaps as early as 300-200 BC. The Nine Chapters on the Mathematical Art ( is a Chinese Mathematics book composed by several generations of scholars from the 10th&ndash2nd century BC and Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Although the author(s) are unknown, they made a huge contribution in the eastern world. The methods were made for everyday life and gradually taught advanced methods. It also contains evidence of the Gaussian elimination. In Linear algebra, Gaussian elimination is an efficient Algorithm for solving systems of linear equations, to find the rank of a matrix
The Suàn shù shū (writings on reckoning) is an ancient Chinese text on mathematics approximately seven thousand characters in length, written on 190 bamboo strips. It was discovered together with other writings in 1983 when archaeologists opened a tomb at Zhangjiashan in Hubei province. Year 1983 ( MCMLXXXIII) was a Common year starting on Saturday (link displays the 1983 Gregorian calendar) Archaeology, archeology, or archæology (from Greek grc ἀρχαιολογία archaiologia – grc ἀρχαῖος archaīos ( Postal map spelling: Hupeh) is a central province of the People's Republic of China. From documentary evidence this tomb is known to have been closed in 186 BC, early in the Western Han dynasty. The Han Dynasty ( 206 BC–220 AD followed the Qin Dynasty and preceded the Three Kingdoms in China. While its relationship to the Nine Chapters is still under discussion by scholars, some of its contents are clearly paralleled there. The text of the Suan shu shu is however much less systematic than the Nine Chapters; and appears to consist of a number of more or less independent short sections of text drawn from a number of sources. Some linguistic hints point back to the Qin dynasty. Not to be confused with the Qing Dynasty, the last dynasty of China
Mathematics in the period of disunity
In the third century Liu Hui wrote his commentary on the Nine Chapters and also wrote Haidao suanjing which dealt with using Pythagorean theorem (already known by the 9 chapters), and triangular measuration to measure the size of things. Liu Hui ( fl 3rd century) was a Chinese Mathematician who lived in the Wei Kingdom. The Sea Island Mathematical Manual or Haidao suanjing (海岛算经 was written by the Chinese mathematican Liu Hui of the Three Kingdoms He was the first Chinese mathematician to calculate Π=3. 1416 with his Π algorithm. Liu Hui's π algorithm is a mathematical algorithm invented by Liu Hui (fl He discovered the usage of Cavalieri's principle to find an accurate formula for the volume of a cylinder, and also developed elements of the integral and the differential calculus during the 3rd century CE. Bonaventura Francesco Cavalieri (in Latin, Cavalerius) ( 1598 - November 30, 1647) was an Italian mathematician The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space Differential Calculus, a field in Mathematics, is the study of how functions change when their inputs change Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives
In the fourth century, another influential mathematician named Zu Chongzhi, introduced the Da Ming Li. Zu Chongzhi ( 429–500 Courtesy name Wenyuan (文遠 was a prominent Chinese mathematician and astronomer during the Liu This calendar was specifically calculated to predict many cosmological cycles that will occur in a period of time. Very little is really known about his life. Today, the only sources are found in the book Sui Shi, we now know that Zu Chongzhi was one of the generations of mathematicians. He computed the value of pi till 7 accurate decimal places (between 3. 1415926 and 3. 1415927) and suggested 355/113 as a good approximate. Along with his son, Zu Geng, Zu Chongzhi used the Cavalieri Method to find an accurate solution for calculationg the volume of the sphere. His work, Zhui Shu was dicarded out of the syllabus of mathematics during the Song dynasty and lost. Many believed that Zhui Shu contains the formulas and methods for linear, matrix algebra, algorithm for calculating the value of Π, formula for the volume of the sphere, and probably integral/differential calculus. The text should also associate with his astronomical methods of interpolation, which would contain knowledge, similar to our modern mathematics.
In the fifth century the manual called "Zhang Qiujian suanjing" discussed linear and quadratic equations. By this point the Chinese had the concept of negative numbers. A negative number is a Number that is less than zero, such as −2 By the Tang Dynasty study of math was fairly standard in the great schools. The Tang Dynasty ( Middle Chinese: dhɑng (June 18 618&ndashJune 4 907 was an imperial dynasty of China preceded by the Sui Dynasty and followed by
Song and Yuan mathematics
Four outstanding mathematicians arose during the Song Dynasty and Yuan Dynasty, particularly in the twelfth and thirteenth centuries: Yang Hui, Qin Jiushao, Li Zhi(Li Ye), and Zhu Shijie. The Song Dynasty ( Wade-Giles: Sung Ch'ao was a ruling dynasty in China between 960&ndash1279 CE it succeeded the Five Dynasties and Ten Kingdoms The Yuan Dynasty ( Pinyin: Yuáncháo Dai Ön Ulus (Дай Юан Улс was a ruling Dynasty founded by the Mongol leader Kublai Yang Hui ( ca 1238–1298 Courtesy name Qianguang (谦光 was a Chinese Mathematician from Qiantang (modern Hangzhou Qin Jiushao ( ca 1202–1261 Courtesy name Daogu (道古 was a Chinese Mathematician born in Ziyang Sichuan, his Zhu Shijie ( fl 13th century) Courtesy name Hanqing (汉卿 Pseudonym Songting (松庭 was one of the greatest Chinese Yang Hui, Qin Jiushao, Zhu Shijie all used the Horner-Ruffini method to solve certain types of simultaneous equations, roots, quadratic, cubic,and quartic equations. In Numerical analysis, the Horner scheme or Horner algorithm, named after William George Horner, is an Algorithm for the efficient evaluation In Mathematics, Ruffini's rule allows the rapid division of any Polynomial by a Binomial of the form x &minus r. Yang Hui was also the first person in history to discover "Pascal's Triangle", along with its binomial proof. \begin{matrix}&&&&&1\\&&&&1&&1\\&&&1&&2&&1\\&&1&&3&&3&&1\\&1&&4&&6&&4&&1\end{matrix Li Zhi on the other hand, investigated on a form of algebraic geometry. His book; Ce Hai Yuan Jing revolutionized the idea of inscribing a circle into triangles, which could be calculated using equations with the Pythagorean theorem. Guo Shoujing of this era also worked on spherical trigonometry for precise astronomical caculations. At this point of mathematical history, a lot of modern western mathematics is already discovered by Chinese mathematicians. Things grew quiet for a time until the thirteenth century Renaissance of Chinese math. This saw Chinese mathematicians solving equations with methods Europe would not know until the eighteenth century. The 18th century lasted from 1701 to 1800 in the Gregorian calendar, in accordance with the Anno Domini / Common Era numbering system The high point of this era came with Zhu Shijie's two books Suanxue qimeng and the Siyuan yujian. Zhu Shijie ( fl 13th century) Courtesy name Hanqing (汉卿 Pseudonym Songting (松庭 was one of the greatest Chinese In one case he reportedly gave a method equivalent to Gauss's pivotal condensation. Johann Carl Friedrich Gauss (ˈɡaʊs, Gauß Carolus Fridericus Gauss ( 30 April 1777 – 23 February 1855) was a German
Qin Jiushao (c. Qin Jiushao ( ca 1202–1261 Courtesy name Daogu (道古 was a Chinese Mathematician born in Ziyang Sichuan, his 1202–1261) was the first to introduce the zero symbol into Chinese mathematics. [9] Before this innovation, blank spaces were used instead of zeros in the system of counting rods. Counting rods ( Japanese: 算木 sangi are small bars typically 3-14 cm long used by mathematicians for calculation in China, Japan [10] Pascal's triangle was first illustrated in China by Yang Hui in his book Xiangjie Jiuzhang Suanfa (详解九章算法), although it was described earlier around 1100 by Jia Xian. \begin{matrix}&&&&&1\\&&&&1&&1\\&&&1&&2&&1\\&&1&&3&&3&&1\\&1&&4&&6&&4&&1\end{matrix Jia Xian (贾宪 was a Chinese mathematician of the Song Dynasty, first half of 11th century [11] Although the Introduction to Computational Studies (算学启蒙) written by Zhu Shijie (fl. Zhu Shijie ( fl 13th century) Courtesy name Hanqing (汉卿 Pseudonym Songting (松庭 was one of the greatest Chinese 13th century) in 1299 contained nothing new in Chinese algebra, it had a great impact on the development of Japanese mathematics. Algebra is a branch of Mathematics concerning the study of structure, relation, and Quantity. In the History of mathematics, Japanese mathematics or wasan (和算 denotes a genuinely distinct kind of mathematics developed in Japan during the [12]
Later developments
However after the overthrow of the Yuan Dynasty China became suspicious of knowledge it used. The Yuan Dynasty ( Pinyin: Yuáncháo Dai Ön Ulus (Дай Юан Улс was a ruling Dynasty founded by the Mongol leader Kublai The Ming Dynasty turned away from math and physics in favor of botany and pharmacology. The Ming Dynasty ( or Empire of the Great Ming ( was the ruling dynasty of China from 1368 to 1644 following the collapse of the Mongol -led Botany, plant science(s, phytology, or plant biology is a branch of Biology and is the scientific study of plant Life Pharmacology (from Greek grc φάρμακον pharmakon, "drug" and grc -λογία -logia) is the study of how Drugs A revival of math in China began in the late nineteenth century, but this was largely based on Western modes of knowledge.
Footnotes and citations
- ^ Chinese overview
- ^ Frank J. Swetz and T. I. Kao: Was Pythagoras Chinese?
- ^ Needham, Volume 3, 91.
- ^ a b c Needham, Volume 3, 92.
- ^ Needham, Volume 3, 92-93.
- ^ Needham, Volume 3, 93.
- ^ Needham, Volume 3, 93-94.
- ^ Needham, Volume 3, 94.
- ^ Joseph Needham, Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth (Taipei: Caves Books, Ltd. , 1986) pp. 43.
- ^ Joseph Needham, Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth (Taipei: Caves Books, Ltd. , 1986) pp. 62–63.
- ^ Needham, Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth (Taipei: Caves Books, Ltd. , 1986) pp. 134–137.
- ^ Joseph Needham, Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth (Taipei: Caves Books, Ltd. , 1986) pp. 46.
Further reading
- Dauben, Joseph W. (2007). "Chinese Mathematics", in Victor J. Katz: The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook. Princeton University Press. ISBN 9780691114859.
- Martzloff, J. (1996). A History of Chinese Mathematics. Springer. ISBN 3-540-33782-2.
External links
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