Chinese mathematics

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Maths in China appeared independently in the 11th century BC. The Chinese independently develop very large and negative numbers, decimals, decimal places value systems, binary systems, algebra, geometry, and trigonometry.

Ancient Chinese mathematicians made progress in the development of algorithms and algebra. While Greek mathematics declined in the west during the Middle Ages, the achievement of Chinese algebra reached its peak in the 13th century, when Zhu Shijie discovered the four unknown method.

As a result of the obvious linguistic and geographical barriers, as well as the content, Chinese mathematics and mathematics of the ancient Mediterranean world were considered to have grown more or less independently until the time when The Nine Chapters on the Mathematical Art reached its final form, while Writings on Reckoning and Huainanzi are roughly contemporary with classical Greek mathematics. Several exchanges of ideas in Asia through known cultural exchanges from at least Roman times are likely. Frequently, the early mathematical elements of society correspond to the imperfect results found later in the branches of modern mathematics such as geometry or number theory. The Pythagorean theorem, for example, has been proven at the time of the Duke of Zhou. Knowledge of the Pascal triangle has also been proven to have existed in China centuries before Pascal, such as Song Dynasty Chinese polymath Shen Kuo.

Video Chinese mathematics

Awal matematika bahasa Mandarin

Simple math on Oracle bone scripts dates back to the Shang Dynasty (1600-1050 BC). One of the oldest surviving mathematical works is Yi Jing , which greatly influenced written literature during the Zhou Dynasty (1050-256 BC). For mathematics, the book includes the use of sophisticated hexagrams. Leibniz shows, I Ching contains elements of binary numbers.

Since the Shang period, the Chinese have fully developed the decimal system. From the earliest days, the Chinese understood basic arithmetic (which dominates far east history), algebra, equations, and negative numbers with counting rods. Although Chinese are more focused on advanced arithmetic and algebra for astronomical use, they are also the first to develop negative numbers, algebraic geometry (Chinese geometry only) and decimal usage.

Mathematics is one of the LiÃÆ'¹ YÃÆ'¬ (??) or Six Arts , students were asked to master during the Zhou Dynasty (1122-256 BC). Learning them all is perfectly required to be the perfect man, or in the Chinese sense, "Renaissance Man". Six Art is rooted in the Confucian philosophy.

The earliest existing work on geometry in China comes from the philosophical Mohammad canon of 330 BC, composed by Mozi followers (470-390 BC). The Mo Jing describes various aspects of many fields related to physical science, and provides little information about math as well. This gives the definition of 'atom' from a geometric point, which states that the line is separated into parts, and the part having no remaining portion (ie can not be divided into smaller parts) and thus forming the extreme end of the line is point. Just as the first and third Euclid definitions and Plato's 'starting line', Mo Jing state that "a point can stand at the end (line) or at first like the presentation of the head at delivery (For transparency) there is no similar to that. "Similar to atomists of Democritus, the Mo Jing states that the dot is the smallest unit, and can not be cut in half, since 'nothing' is indivisible. It states that two lines of the same length will always end in the same place, while defining for long comparison and for alignment , together with the principle of space and space constrained.. It also illustrates the fact that aircraft without quality thickness can not be stacked because they can not touch each other. This book provides word recognition for circumference, diameter, and radius, along with the volume definition.

The history of mathematical development has no evidence. There is still a debate about certain classical mathematics. For example, the date of Zhoubi Suanjing is about 1200-1000 BC, but many scholars believe it was written between 300-250 BC. The Zhoubi Suanjing contains in-depth evidence of Gougu Theorem (special case of Pythagoras Theorem) but rather focuses on astronomical calculations. However, recent archaeological discoveries from the Tsinghua Bamboo Slip, dated c. 305 BC, has revealed some aspects of pre-Qin mathematics, such as the first known decimal multiplication table.

Abacus was first mentioned in the 2nd century BC, in addition to the 'stem calculation' ( suan zi ) in which a small bamboo stick is placed in a box of consecutive boxes.

Maps Chinese mathematics

Qin math

Not much is known about the mathematics of the Qin dynasty, or earlier, because of the burning of books and the burial of scholars, circa 213-210 BC. Knowledge of this period can be determined from civil projects and historical evidence. The Qin Dynasty created a standard system of weights. Civil projects of the Qin dynasty are significant achievements of human engineering. Emperor Qin Shihuang (???) ordered many people to build large and living statues for the palace tomb along with other temples and shrines, and the shape of the tomb was designed with architectural geometric skills. It is certain that one of the greatest achievements in human history, the Great Wall of China, requires many mathematical techniques. All Qin dynasty buildings and large projects use advanced calculation formulas for volume, breadth and proportion.

Qin bamboo money was bought at Hong Kong's antique market by Yuelu Academy, according to preliminary reports, containing the earliest epigraphic samples of mathematical treatises.

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Han Mathematics

In the Han Dynasty, the numbers were developed into a decimal place value system and used on a counting board with a set of counting bars called chousuan, consisting of only nine symbols with blank space on a counting board representing zero. The mathematicians Liu Xin (d.23) and Zhang Heng (78-139) gave a more accurate estimate for pi than the Chinese from the previous century had been used. Zhang also applied mathematics in his work in astronomy. Hundreds of examples of practical use of mathematics by Qin and Han administrators have been unearthed, proving that many of the topics covered in the theoretical treatises are actually being used.

Suan shu shu

The SuÃÆ'n shÃÆ'¹ sh? (writing about calculations) is an ancient Chinese text about mathematics that is about seven thousand characters long, written on 190 pieces of bamboo. It was found along with other writings in 1984 when archaeologists opened a tomb in Zhangjiashan in Hubei province. From documentary evidence, this tomb is known to have been closed in 186 BC, at the beginning of the Western Han dynasty. While its relationship to the Nine Chap is still under discussion by experts, some of its contents are clearly parallel there. However, the text of Suan shu shu is much less systematic than Nine Chapters, and appears to consist of a number of short sections of a more or less independent text drawn from a number of sources. Some linguistic clues lead back to the Qin dynasty.

In the basic mathematical example at SuÃÆ'n shÃÆ'¹ sh? , the square root is estimated using the "advantages and disadvantages" that say to "combine the advantages and disadvantages of dividing; (taking) deficient counters multiplied by excess denominators and overdeliver multiplies denominator deficiency, combine them as dividends."

Nine Chapters on Mathematical Art

The Nine Chapters on Mathematical Art is China's mathematical book, the oldest archaeological remains in 179 AD (usually dated 1000 BC), but probably as early as 300-200 BC. Although the author is unknown, they make a major contribution in the eastern world. Methods are made for everyday life and gradually teach advanced methods. It also contains evidence of Gaussian Elimination and Cramer Rules for a system of linear equations.

Nine Chapters on Mathematical Art is one of China's most influential mathematical books and consists of about 246 problems. Chapter eight discusses the solving of determinative and indefinite linear equations using positive and negative numbers, with one problem handling the settlement of four equations in five unknowns. Estimates of Chou Pei Suan Ching, generally regarded as the oldest of classical maths, differ by almost a thousand years. The date around 300 BC would seem reasonable, thus placing it in a fierce competition with other treatises, Jiu zhang suanshu, comprising about 250 BC, that is, shortly before the Han dynasty (202 BC). Almost as old in Chou Pei, and perhaps the most influential of all Chinese math books, is Jiuzhang suanshu, or Nine Chapters on the Art of Mathematics. This book covers 246 issues in surveys, agriculture, partnerships, engineering, taxation, computation, equation solutions, and the properties of right triangles. Chapter eight of the Nine chapters is essential for simultaneous problem solution of linear equations, using positive and negative numbers. The earliest known magic box appeared in China. The Chinese especially like the pattern, as the natural result of arranging the counting rods in lines on the counting board to perform the calculations; therefore, it is not surprising that the first record (ancient but unknown origin) of the magic box appears there. Attention to such patterns leads the author of Nine Chapter to solve the system of linear equations by placing the coefficients and constants of the linear equations into the matrix and performing a column reduction operation on the matrix to reduce them to the triangular shape represented by the equation < span> ${\ displaystyle 36z = 99}$ , ${\ displaystyle 5y z = 24}$ , and ${\ displaystyle 3x 2y z = 39}$ from where ${\ displaystyle z}$ , ${\ displaystyle y}$ , and ${\ displaystyle x}$ successively found easily. The final problem in this chapter involves four equations in five unknowns, and the topic of uncertain equations is still a favorite among Oriental societies.

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Math in split period

In the third century Liu Hui wrote his commentary on the Nine Chapters and also wrote Haidao Suanjing which discusses the use of the Pythagoras theorem (already known by 9 chapters), and triples triangulation for the survey; his achievements in mathematical surveys exceed those reached in the west by the millennium. He is the first Chinese mathematician to calculate ? = 3.1416 with algorithm ? . He found the use of the Cavalieri principle to find accurate formulas for cylindrical volumes, and also developed the integral and differential elements of calculus during the 3rd century.

In the fourth century, another influential mathematician named Zu Chongzhi introduced Da Ming Li. This calendar is specifically calculated to predict many cosmological cycles that will occur over a period of time. Very little is known about his life. Today, the only source found in Sui, we now know that Zu Chongzhi was one of the generations of mathematicians. He used the Liu Hui pi-algorithm applied to 12288-gon and obtained the pi value to 7 accurate decimal places (between 3.1415926 and 3.1415927), which would still be the most accurate approach? available for the next 900 years. He also used He Chengtian's interpolation method to approach irrational numbers with fractions in his astronomical and mathematical works, he obtained ${\ displaystyle {\ tfrac {355} {113}}}$ as a good fractional forecast for pi; Yoshio Mikami commented that neither the Greeks, nor the Hindus and Arabs knew about this fractional approach to pi, not until the Dutch mathematician Adrian Anthoniszoom rediscovered it in 1585, "the Chinese had possessed this most extraordinary of all fractional values ​​over the entire millennium earlier than Europe "

Together with his son Zu Geng, Zu Chongzhi used the Cavalieri Method to find an accurate solution to calculate the volume of the ball. In addition to containing formulas for spherical volumes, the book also includes the formula of cubic equations and the accurate value of pi. His work, Zhui Shu was removed from the mathematical syllabus during the Song dynasty and was lost. Many believe that Zhui Shu contains formulas and methods for linear, algebraic matrices, algorithms for calculating the value of ? , the formula for spherical volume. The text must also be associated with astronomical interpolation methods, which will contain knowledge, similar to our modern mathematics.

A mathematical manual called "Sunzi classical mathematics" dated between 200--400Ã, CE contains the most detailed step-by-step description of the multiplication algorithm and the division by the counting rod. The earliest records of multiplication and division algorithms using Arabic Hindu numerals were written in writing by Al Khawarizmi in the early 9th century. Khwarizmi's step by step algorithm is completely identical to the Sunzi division algorithm described in classical Sunzi mathematics four centuries earlier. Khwarizmi's work was translated into Latin in the 13th century and spread to the west, the later division algorithm evolved into the Galley division. The arithmetic transmission route where the Chinese decimal places know how to the west is unclear, how the division and Sunzi's multiplexing algorithm with the stems calculus ends in the form of Hindu Arabic numerals in Khwarizmi's work is unclear, since Al Khawarizmi never gives any Sanskrit sources not quoted. every Sanskrit verse. However, the effect of stem calculus on the Hindu division is evident, for example in the division example, 324 must be 32400, only the stalk calculus used is empty for zero.

In the fifth century, the manual called "Zhang Qiujian suanjing" discussed linear and quadratic equations. At this point the Chinese have the concept of a negative number.

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Maths Tang

By the study of Tang dynasty mathematics is quite standard in large schools. The Ten Canon Computing is a collection of ten Chinese mathematical works, composed by early Tang Dynasty mathematicians Li Chunfeng (??? 602-670), as the official mathematical text for imperial examinations in mathematics. Sui and Tang dynasties run the "School of Computing".

Wang Xiaotong was a great mathematician at the beginning of the Tang Dynasty, and he wrote a book: Jigu Suanjing ( Continuation of Ancient Mathematics ), where numerical solutions to which cubic equations commonly appear for the first time

The Tibetans gained their first knowledge of the mathematics (arithmetic) of China during the reign of Nam-ri srong btsan, who died in 630.

The sine table by Indian mathematician Aryabhata was translated into the Chinese mathematical book of Kaiyuan Zhanjing, which was composed in 718 CE during the Tang Dynasty. Although the Chinese excel in other fields of mathematics such as solid geometry, binomial theorems, and complex algebraic formulas, early forms of trigonometry are not much appreciated as in Indian mathematics and contemporary Islam.

Yi Xing, mathematicians and Buddhist monks are credited for counting tangent tables. In contrast, early Chinese used an empirical substitute known as chong cha , while the practical use of aircraft trigonometry in using sinus, tangent, and cutoffs was known. Yi Xing is famous for his genius, and is known to have counted the number of possible positions on a go board game (though without a symbol for zero he had difficulty in revealing numbers).

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Songs and math Yuan

Northern Song Dynasty mathematician Jia Xian developed an additive multiplication method for extracting square and cubic roots that implements the "Horner" rule.

Four outstanding mathematicians emerged during the Song and Yuan Dynasties, especially in the twelfth and thirteenth centuries: Yang Hui, Qin Jiushao, Li Zhi (Li Ye), and Zhu Shijie. Yang Hui, Qin Jiushao, Zhu Shijie all used Horner-Ruffini methods six hundred years earlier to solve some simultaneous equations, roots, squares, cubic, and quartic. Yang Hui was also the first person in history to discover and prove the "Pascal Triangle", along with its binomial evidence (though the earliest mention of the Pascal triangle in China existed before the eleventh century AD). Li Zhi on the other hand, investigates on the shape of algebraic geometry based on Tian yuan shu. Her book; Ceyuan haijing revolutionized the idea of ​​writing a circle into a triangle, altering the problem of geometry with algebra rather than the traditional method of using Pythagorean theorem. Guo Shoujing this era also works on spherical trigonometry for precise astronomical calculations. At this point in the history of mathematics, much of modern western mathematics has been discovered by Chinese mathematicians. Everything became quiet for a while until the Renaissance of thirteenth-century Chinese mathematics. This view of Chinese mathematicians solving equations with European methods would not have known until the eighteenth century. The highest point of this era comes with two books of Zhu Shijie Suanxue qimeng and Siyuan yujian . In one case he reportedly provided a method equivalent to Gauss' essential condensation.

Qin Jiushao (c: 1202-1261) was the first to introduce a zero symbol into Chinese mathematics. Prior to this innovation, the blank space was used instead of zero in the stem counting system. One of Qin Jiushao's most important contributions is his method of solving high-order equations. Referring to Qin's solution of the 4th order equation, Yoshio Mikami said: "Who can deny the fact of the famous process of Horner used in China at least nearly six centuries long earlier than in Europe?" Qin also solves the 10th order equation.

The Pascal Triangle was first illustrated in China by Yang Hui in his book Xiangjie Jiuzhang Suanfa (??????), although described earlier about 1100 by Jia Xian. Although the Introduction to Computational Studies (????) written by Zhu Shijie (13th century) in 1299 did not contain any novelty in Chinese algebra, it had a major impact on the development of Japanese mathematics.

Algebra

Ceyuan haijing

Ceyuan haijing (pinyin: CÃÆ'¨yuÃÆ'¡n H? ijÃÆ' ¬ ng) (Chinese character: ????), or Sea Mirror Measuring Circle , is a collection of 692 formulas and 170 problems related to written circles in triangles, written by Li Zhi (or Li Ye) (1192-1272 AD). He uses Tian yuan shu to transform complicated geometry problems into pure algebra problems. He then uses a fanfold, or Horner's method, to solve equations of as high as six degrees, although he does not explain his method of solving equations. "Li Chih (or Li Yeh, 1192-1279), a Peking mathematician who was offered a government post by Khublai Khan in 1206, but politely found a reason to reject it. Ts'e-yuan hai-ching ( Sea-Mirror of the Circle Measurements ) includes 170 problems relating to [...] some problems that cause the polynomial equation of the sixth level.Although it does not explain the method of solution equation, from those used by Chu Shih-chieh and Horner. Other people who use the Horner method are Ch'in Chiu-shao (ca. 1202 - ca.1261) and Yang Hui (fl., ca. 1261-1275).

Jade Mirror of Four Unknowns

Si-yÃÆ'¼an yÃÆ'¼-jian (??????), or Jade Mirror of Four Unknowns , written by Zhu Shijie in 1303 AD and marks the peak of the development of Chinese algebra. The four elements, called heaven, earth, man and matter, represent four unknown quantities in the algebraic equation. This corresponds to a simultaneous equation and with a fourteen degree equation. The author uses the fan fa method, today called the Horner method, to solve this equation.

The Jade Mirror opens with an arithmetic triangle diagram (Pascal Triangle) using a zero round symbol, but Chu Shih-chieh denies credit for it. A similar triangle appears in Yang Hui's work, but without the zero symbol.

Ada banyak persamaan seri penjumlahan yang diberikan tanpa bukti di Cermin Berharga . Beberapa seri penjumlahan adalah:

${\ displaystyle 1 ^ {2} 2 ^ {2} 3 ^ {2} \ cdots n ^ {2} = {n (n 1) ( 2n 1) \ over 3!}}  ÂÂ$

${\ displaystyle 1 8 30 80 \ cdots {n ^ {2} (n 1) (n 2) \ over 3!} = {n (n 1) (n 2) (n 3) (4n 1) \ over 5!}}  ÂÂ$

Risalah Matematika di Sembilan Bagian

Shu-shu chiu-chang , or The Mathematics of Nine Sections , written by rich governor and minister Ch'in Chiu-shao (ca. 1202 - ca. 1261 AD) and with the discovery of simultaneous congruence solving methods, it marks a high point in Chinese indeterminate analysis.

Magic box and magic circle

The most famous original magic boxes ordered over three are associated with Yang Hui (fl. Ca 1261-1275), who work with magic boxes as tall as ten. He also works with magic circles.

Trigonometry

The trigonometric embryonic state in China slowly began to change and increase during the Song Dynasty (960-1279), in which Chinese mathematicians began to express a greater emphasis on the needs of spherical trigonometry in calendarical science and astronomical calculations. The Chinese scientist polymath, mathematician and official Shen Kuo (1031-1095) used trigonometric functions to solve mathematical problems of chords and arcs. Victor J. Katz writes that in the Shen formula "intersecting circle technique", he creates an arc forecast of the circle s by s = c 2 < i> v ² / d , with d the diameter, v is versine, c is the length of the subcending arc chord c . Sal Restivo writes that Shen's work in arc circles provides the basis for spherical trigonometry developed in the 13th century by mathematician and astronomer Guo Shoujing (1231-1316). As historian L. Gauchet and Joseph Needham, Guo Shoujing uses spherical trigonometry in his calculations to improve the Chinese calendar and astronomical system. Along with seventeenth-century Chinese illustrations from Guo's mathematical evidence, Needham states that:

Guo uses a rectangular pyramid, a rectangular basal consisting of an equatorial equator and an ecliptic arc, together with two meridian arcs, one of which passes through the summer solstice point... By such a method he is able to obtain du lÃÆ'¼ (degrees equator with a degree of ecliptic), ji cha (chord values ​​for a particular ecliptic arc), and cha lÃÆ'¼ (the difference between arc chords is different from 1 degree).

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Imperial Imperial Development

After the overthrow of the Yuan Dynasty, China became suspicious of the knowledge it employed. The Ming Dynasty turned away from mathematics and physics for the sake of botany and pharmacology.

In this period, the abacus first mentioned in the second century BC along with the 'calculation with the stick' ( suan zi ) now enters into the form suan pan and goes beyond the stem count and into a preferred computing device. Zhu Zaiyu, Prince Zheng who created the same temperament used 81 abacus positions to calculate square roots and cubic roots from 2 to 25 numerical accuracy.

Although the transition from stem counting to abacus allows to reduce the calculation time, it may also lead to stagnation and the decline of Chinese mathematics. The rich layout patterns of counting the number of rods on counting boards inspired many Chinese discoveries in mathematics, such as the principle of cross-fraction multiplexing and methods for solving linear equations. Similarly, Japanese mathematicians are influenced by the numerical stack count layout in their definition of the matrix concept. However, during the Ming dynasty, mathematicians were fascinated by perfecting the algorithm for the abacus. Thus, many works devoted to abacus mathematics arose in this period; at the expense of creating new ideas.

Despite Shen and Guo's work accomplishments in trigonometry, other important work in Chinese trigonometry will not be published until 1607, with the publication of Euclid's Elements by Chinese officials and astronomers Xu Guangqi (1562-1633). ) and Italian Jesuit Matteo Ricci (1552-1610).

The rise of mathematics in China began in the late nineteenth century, when Joseph Edkins, Alexander Wylie and Li Shanlan translated astronomical, algebraic, and integral differential-integrative works into Chinese, published by the London Missionary Press in Shanghai.

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Modern Chinese Math

Chinese mathematics experienced a wave of great revival after the establishment of a modern Chinese republic in 1912. Since then, modern Chinese mathematicians have made many achievements in various fields of mathematics.

Some notable Chinese ethnic mathematicians include:

• Shiing-Shen Chern is widely regarded as a leader in geometry and one of the greatest mathematicians of the 20th century and was awarded the Wolves prize for the contribution of mathematics in large numbers.
• Ky Fan, made a large number of fundamental contributions to various areas of mathematics. His work in fixed point theory, in addition to influencing nonlinear functional analysis, has found extensive applications in mathematical economics and game theory, potential theory, calculus of variations, and differential equations.
• Shing-Tung Yau, his contribution has influenced physics and mathematics, and he has been active in the interface between geometry and theoretical physics and subsequently rewards Fields medals for his contributions.
• Terence Tao, a talented Chinese ethnic boy who received his master's degree at the age of 16, was the youngest participant in the entire history of the International Mathematics Olympiad, first competing at the age of ten, winning bronze, silver, and gold medals. He remains the youngest winner of each of the three medals in Olympiad history. He will continue to receive Fields medals.
• Yitang Zhang, a number theorist who founded the first is confined to the gap between prime numbers.
• Chen Jingrun, number theorist who proves Chen's theorem, a step towards Goldbach's alleged.

Performance on IMO

Compared to other participating countries at the International Mathematics Olympiad, China has the highest team scores and won all-gold member IMOs with full teams at most times.

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Math text

Dinasti Zhou

Zhoubi Suanjing c. 1000 BCE-100 CE

• Teori astronomi, dan teknik perhitungan
• Bukti teorema Pythagoras (Shang Gao Theorem)
• Perhitungan pecahan
• Teorema Pythagoras untuk tujuan astronomi

Nine Chapter about Mathematical Arts 1000 BC? - 50Ã, CE

• ch.1, computational algorithm, field number field, GCF, LCD
• chapter 2, proportion
• bag.3, proportion
• ch.4, square, cube root, find unknown
• ch.5, volume and use pi as 3
• bag.6, proportion
• ch, 7, interdetermination equation
• ch.8, elimination and Gauss matrix
• ch.9, Pythagorean Theorem (Gougu's Theorem)

Dinasti Han

Book on Figures and Calculations 202 BC-186 BC

• Calculate the volume of different 3-dimensional shapes
• Calculation of unknown side of rectangle, given area and one side
• Use the wrong positioning method to find the root and extraction of the approximate square root
• Conversions between different units

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Mathematics in education

Source of the article : Wikipedia