Chinese Contributions to Science and Mathematics

[Type 052D]

Let's Start of with 祖沖之/祖冲之 (Zǔ Chōngzh&#299

His mathematical achievements included:

-the Daming calendar (大明&#26310 introduced by him in 465 A.D.

-distinguishing the Sidereal Year and the Tropical Year, and he measured 45 years and 11 months per degree between those two, and today we know the difference is 70.7 years per degree.

-calculating one year as 365.24281481 days, which is very close to 365.24219878 days as we know today.

-calculating the number of overlaps between sun and moon as 27.21223, which is very close to 27.21222 as we know today; using this number he successfully predicted an eclipse four times during 23 years (from 436 to 459).

-calculating the Jupiter year as about 11.858 Earth years, which is very close to 11.862 as we know of today.

-deriving two approximations of pi, (3.1415926538932...) which held as the most accurate approximation for π for over nine hundred years. His best approximation was between 3.1415926 and 3.1415927, with 355⁄113 (密率, Milü, detailed approximation) and 22⁄7 (約率, Yuelü, rough approximation) being the other notable approximations. He obtained the result by approximating a circle with a 12,288 (= 212 × 3) sided polygon. This was an impressive feat for the time, especially considering that the device Counting rods he used for recording intermediate results were merely a pile of wooden sticks laid out in certain patterns. Japanese mathematician Yoshio Mikami pointed out, " was nothing more than the π value obtained several hundred years earlier by the Greek mathematician Archimedes, however Milu could not be found in any Greek, Indian or Arabian manuscripts, not until 1585 Dutch mathematician Adriaan Anthoniszoom obtained this fraction; the Chinese possessed this most extraordinary fraction over a whole millennium earlier than Europe". Hence Mikami strongly urged that the fraction be named after Zu Chongzhi as Zu Chongzhi fraction. In Chinese literature, this fraction is known as "Zu rate". Zu rate is a best rational approximation to π, and is the closest rational approximation to π from all fractions with denominator less than 16600.

-finding the volume of a sphere as πD3/6 where D is diameter (equivalent to 4πr3/3).

 

[Type 052D]

Next mathematician is Liu Hui:

Liu Hui (fl. 3rd century) was a mathematician of the state of Cao Wei during the Three Kingdoms period of Chinese history.
Along with Zu Chongzhi (429–500), Liu Hui was known as one of the greatest mathematicians of ancient China.

Liu Hui presented, in a separate appendix of 263 AD called Haidao suanjing or The Sea Island Mathematical Manual, several problems related to surveying. This book contained many practical problems of geometry, including the measurement of the heights of Chinese pagoda towers. This smaller work outlined instructions on how to measure distances and heights with "tall surveyor's poles and horizontal bars fixed at right angles to them". With this, the following cases are considered in his work:

-The measurement of the height of an island opposed to its sea level and viewed from the sea
-The height of a tree on a hill
-The size of a city wall viewed at a long distance
-The depth of a ravine (using hence-forward cross-bars)
-The height of a tower on a plain seen from a hill
-The breadth of a river-mouth seen from a distance on land
-The depth of a transparent pool
-The width of a river as seen from a hill
-The size of a city seen from a mountain.

 

[Type 052D]

The Nine Chapters on the Mathematical Art/ 九章算术

The full title of The Nine Chapters on the Mathematical Art appears on two bronze standard measures which are dated to 179 CE, but there is speculation that the same book existed beforehand under different titles.

Contents of the Nine Chapters are as follows:
方田 Fangtian - Rectangular fields. Areas of fields of various shapes; manipulation of vulgar fractions.
粟米 Sumi - Millet and rice. Exchange of commodities at different rates; pricing.
衰分 Cuifen - Proportional distribution. Distribution of commodities and money at proportional rates.
少廣 Shaoguang - The lesser breadth. Division by mixed numbers; extraction of square and cube roots; dimensions, area and volume of circle and sphere.
商功 Shanggong - Consultations on works. Volumes of solids of various shapes.
均輸 Junshu - Equitable taxation. More advanced problems on proportion.
盈不足 Yingbuzu - Excess and deficit. Linear problems solved using the principle known later in the West as the rule of false position.
方程 Fangcheng - The rectangular array. Systems of linear equations, solved by a principle similar to Gaussian elimination.
勾股 Gougu - Base and altitude. Problems involving the principle known in the West as the Pythagorean theorem.

Can Chinese members contribute please? Thanks!

 

[Okemos]

China's achievements are remarkable in ancient time, considering China had no outside interaction, i.e. "technology transfer" as some people love to use. China on its own, alone in the Far East, developed its unique human civilization, while the rest of the old world had so much interaction with each other.

Nowadays, due to dominance of European civilization, most achievements in ancient times are attributed to Greece and its derivatives, even though similar discoveries were already made in the Far East, at the same time, or even earlier.

But I don't think it really matters except for empty pride and irrational nationalism. We should strive to relive our glorious past.

 

[AViet]

We are not the Far East to anyone, we are East Asia. Far East is Euro-centric word. Please use the correct term.

 

[AUSTERLITZ]

Very nice.Chinese history is sometimes difficult for outsiders mostly due to difficult names.

 

[Type 052D]

China's achievements are remarkable in ancient time, considering China had no outside interaction, i.e. "technology transfer" as some people love to use. China on its own, alone in the Far East, developed its unique human civilization, while the rest of the old world had so much interaction with each other.

Nowadays, due to dominance of European civilization, most achievements in ancient times are attributed to Greece and its derivatives, even though similar discoveries were already made in the Far East, at the same time, or even earlier.

But I don't think it really matters except for empty pride and irrational nationalism. We should strive to relive our glorious past.

Here is an good example of that statement of yours:

Zhang Heng

Zhang Heng (simplified Chinese: 张衡; traditional Chinese: 張&#34913 was a Chinese astronomer, mathematician, inventor, geographer, cartographer, artist, poet, statesman, and literary scholar from Nanyang, Henan. He lived during the Eastern Han Dynasty (AD 25–220) of China. He was educated in the capital cities of Luoyang and Chang'an, and began his career as a minor civil servant in Nanyang. Eventually, he became Chief Astronomer, Prefect of the Majors for Official Carriages, and then Palace Attendant at the imperial court.
Zhang applied his extensive knowledge of mechanics and gears in several of his inventions. He invented the world's first water-powered armillary sphere, to represent astronomical observation;[1] improved the inflow water clock by adding another tank;[2] and invented the world's first seismometer, which discerned the cardinal direction of an earthquake 500 km (310 mi) away. Furthermore, he improved previous Chinese calculations of the formula for pi. In addition to documenting about 2,500 stars in his extensive star catalogue, Zhang also posited theories about the Moon and its relationship to the Sun; specifically, he discussed the Moon's sphericity, its illumination by reflecting sunlight on one side and remaining dark on the other, and the nature of solar and lunar eclipses. His fu (rhapsody) and shi poetry were renowned and commented on by later Chinese writers. Zhang received many posthumous honors for his scholarship and ingenuity, and is considered a polymath by some scholars. Some modern scholars have also compared his work in astronomy to that of Ptolemy (AD 86–161).

For centuries the Chinese approximated pi as 3; Liu Xin (d. AD 23) made the first known Chinese attempt at a more accurate calculation of 3.1457, but there is no record detailing the method he used to obtain this figure. In his work around 130, Zhang Heng compared the celestial circle to the diameter of the earth, proportioning the former as 736 and the latter as 232, thus calculating pi as 3.1724. In Zhang's day, the ratio 4:3 was given for the area of a square to the area of its inscribed circle and the volume of a cube and volume of the inscribed sphere should also be 42:32. In formula, with D as diameter and V as volume, D3:V = 16:9 or V=D3; Zhang realized that the value for diameter in this formula was inaccurate, noting the discrepancy as the value taken for the ratio. Zhang then attempted to remedy this by amending the formula with an additional D3, hence V=D3 + D3 = D3. With the ratio of the volume of the cube to the inscribed sphere at 8:5, the implied ratio of the area of the square to the circle is √8:√5. From this formula, Zhang calculated pi as the square root of 10 (or approximately 3.162). Zhang also calculated pi as = 3.1466 in his book Ling Xian (靈&#25010. In the 3rd century, Liu Hui made the calculation more accurate with his π algorithm, which allowed him to obtain the value 3.14159. Later, Zu Chongzhi (429–500) approximated pi as or 3.141592, the most accurate calculation for pi the ancient Chinese would achieve.

Water-powered armillary sphere

Zhang Heng is the first person known to have applied hydraulic motive power (i.e. by employing a waterwheel and clepsydra) to rotate an armillary sphere, an astronomical instrument representing the celestial sphere. The Greek astronomer Eratosthenes (276–194 BC) invented the first armillary sphere in 255 BC. The Chinese armillary sphere was fully developed by 52 BC, with the astronomer Geng Shouchang's addition of a permanently fixed equatorial ring. In AD 84 the astronomers Fu An and Jia Kui added the ecliptic ring, and finally Zhang Heng added the horizon and meridian rings. This invention is described and attributed to Zhang in quotations by Hsu Chen and Li Shan, referencing his book Lou Shui Chuan Hun Thien I Chieh (Apparatus for Rotating an Armillary Sphere by Clepsydra Water). It was likely not an actual book by Zhang, but a chapter from his Hun I or Hun I Thu Chu, written in 117 AD. His water-powered armillary influenced the design of later Chinese water clocks and led to the discovery of the escapement mechanism by the 8th century. The historian Joseph Needham (1900–1995) states:
"What were the factors leading to the first escapement clock in China? The chief tradition leading to Yi Xing (AD 725 ) was of course the succession of 'pre-clocks' which had started with Zhang Heng about 125. Reason has been given for believing that these applied power to the slow turning movement of computational armillary spheres and celestial globes by means of a water-wheel using clepsydra drip, which intermittently exerted the force of a lug to act on the teeth of a wheel on a polar-axis shaft. Zhang Heng in his turn had composed this arrangement by uniting the armillary rings of his predecessors into the equatorial armillary sphere, and combining it with the principles of the water-mills and hydraulic trip-hammers which had become so widespread in Chinese culture in the previous century."

 

[yusheng]

The Nine Chapters on the Mathematical Art/ 九章算术

read this book,
The Nine Chapters on the Mathematical Art: Companion and Commentary [Hardcover]
Shen Kangshen (Editor), John N. Crossley (Editor), Anthony W. -C. Lun (Editor)


The Nine Chapters on the Mathematical Art has been the most important mathematical source in China for the past 2000 years, comparable in significance to Euclid's Elements in the West. The Nine Chapters quickly acquired a distinguished reputation, and was the standard mathematics textbook in China and the surrounding regions until Western science was introduced in about 1600. This volume contains the first complete English translation of the Nine Chapters, together with the illuminating commentary of Liu Hui written in the 3rd century AD and other early century commentaries and further insights provided by the translators. The Nine Chapters contains 246 problems and their solutions, which fall into nine categories that are firmly based on practical needs. There are methods for solving problems in areas such as land measurement, construction, agriculture, commerce, and taxation, while the Chinese commentators provide the algorithms needed to solve the problems, and explanations of how the algorithms work. The translators' commentary provides clear and accessible background material for the Western reader, explanations of technicalities, and notes on the treatment of similar or identical mathematical problems in other countries. This first, full-English translation gives us an idea of the distinctive style and important contributions that have been made by traditional Chinese mathematics.

Review
"The Nine Chapters is a classic of Chinese mathematics ... it will be of great value to scholars with an interest in Chinese mathematics and more generally to students of ancient mathematics" Proceedings of the Edinburgh Mathematical Society
Language Notes
Text: English (translation)
Original Language: Chinese
See all Editorial Reviews

--------------------------------------------------------------------------------
Product Details
Hardcover: 616 pages
Publisher: Oxford University Press, USA (January 20, 2000)
Language: English
ISBN-10: 0198539363
ISBN-13: 978-0198539360
Product Dimensions: 1.5 x 6.3 x 9 inches
Shipping Weight: 2.2 pounds (View shipping rates and policies)

 

[Fsjal]

I personally hate maths. I am more of a literature person, since I find the subject English easier than Maths.

 

[Type 052D]

I personally hate maths. I am more of a literature person, since I find the subject English easier than Maths.

I used to terrible at maths but I worked hard because I loved sciences, if you put hard work into Mathematics then I'm 100% sure that you will be good at maths. Just do practice after practice and you will be great at Mathematical problem solving.

 

[Wright]

We are not the Far East to anyone, we are East Asia. Far East is Euro-centric word. Please use the correct term.

Unless you are Korean, East Asia does not include Vietnam. East Asia is a Racial and cultural designation encompassing Japan, China, Korea.

Vietnam along with Thailand, are termed "South east Asia'

 

[AViet]

Unless you are Korean, East Asia does not include Vietnam. East Asia is a Racial and cultural designation encompassing Japan, China, Korea.

Vietnam along with Thailand, are termed "South east Asia'[/QUOTE

I guess you only know Vietnam on TV or book.

Racially, Vietnamese (especially northern Vietnamese) is the same as South Chinese. The Nam Viet (Nanyue) kingdom (traditional Vietnamese historians viewed it as the first independent Viet kingdom) have its capital in today Guangzhou. When Trung sisters revolted against Han Chinese in 40 AD, their followers includes people from Guangxi, Guangdong and Hainan provinces of China. My sister-in-law, a Hanoian, is an ethnic Nung (ethnic Zhuang in China).

Culturally, Vietnamese is much closer to Chinese than to any South East Asian.

3/4 land of Russia belongs to Asia continent, that does not make Russian Asian.

 

[Wholegrain]

Unless you are Korean, East Asia does not include Vietnam. East Asia is a Racial and cultural designation encompassing Japan, China, Korea.

Vietnam along with Thailand, are termed "South east Asia'[/QUOTE

I guess you only know Vietnam on TV or book.

Racially, Vietnamese (especially northern Vietnamese) is the same as South Chinese. The Nan Viet kingdom (traditional Vietnamese historians viewed it as the first independent Viet kingdom) have its capital in today Guangzhou. When Trung sisters revolted against Han Chinese in 40 AD, their followers includes people from Guangxi, Guangdong and Hainan provinces of China. My sister-in-law, a Hanoian, is an ethnic Nung (ethnic Zhuang in China).

Culturally, Vietnamese is much closer to Chinese than to any South East Asian.

3/4 land of Russia belongs to Asia continent, that does not make Russian Asian.

Văn Lang and Au Lac were the fisrt Vietnamese Kingdoms, Nanyue was founded by a Chinese and it conquered Au Lac.

Southern Chinese paternal lineage (y chromosome) is the same as northern Chinese. Most southern Chinese are descended from northern Chinese men marrying native (Baiyue) women, so the maternal (mitochondrial DNA) and autosomnal DNA will be similar to Vietnamese and other southern mongoloid peoples.

In Chinese and Vietnamese culture, descent is traced through the paternal line. Anyway most Baiyue were not ethnic Vietnamese, they are just related people.

We may have the same race morphologically because our maternal descent is heavily from the baiyue natives of southern China but our paternal lines are mostly from northern Chinese and we are one people (with northern Chinese) because of that. We are not Vietnamese people. Our subgroup of Y chromosome Haplogroup O is different from Vietnamese and its common to both northern and southern Chinese. We also do not share paternal ancestry with Mongols because they are Haplogroup C.

 

[cirr]

This is not a thread about the delineation and division of Asia。

This is a thread about ancient science and civilization in China。

For those who are interested：

The Genius of China: 3,000 Years of Science, Discovery, and Invention

Amazon.com: The Genius of China: 3,000 Years of Science, Discovery, and Invention (9781594772177): Robert Temple, Joseph Needham: Books

Revised, full-color illustrated edition of the multi-award-winning, international bestseller that charts the unparalleled and astounding achievement of ancient China

• Brings to life one hundred Chinese “firsts” in the fields of agriculture, astronomy, engineering, mathematics, medicine, music, technology, and warfare

• Based on the definitive work of the world’s most famous Sinologist, Joseph Needham (1900-1995), author of Science and Civilisation in China

• Organized by field, invention, and discovery for ease of reference

Undisputed masters of invention and discovery for 3,000 years, the ancient Chinese were the first to discover the solar wind and the circulation of the blood and even to isolate sex hormones. From the suspension bridge and the seismograph to deep drilling for natural gas, the iron plough, and the parachute, ancient China’s contributions in the fields of engineering, medicine, technology, mathematics, science, transportation, warfare, and music helped inspire the European agricultural and industrial revolutions.

Since its original publication, The Genius of China has won five literary awards in America and been translated into 43 languages. Its Chinese edition, The Spirit of Chinese Invention, was approved by the Chinese Ministry of Education for use in connection with the national secondary curriculum in China. Based on the immense, authoritative scholarship of the late Joseph Needham, the world’s foremost scholar of Chinese science, and including a foreword by him, this revised full-color illustrated edition brings to life the spirit and excitement of the unparalleled achievements of ancient China.

 

[Type 052D]

Unless you are Korean, East Asia does not include Vietnam. East Asia is a Racial and cultural designation encompassing Japan, China, Korea.

Vietnam along with Thailand, are termed "South east Asia'

Vietnam was part of the Sinoshphere before Japan even had the Hanzi written script (Kanji) in the 7th century. Vietnam was part of the Han Dynasty tributary system. They used Han characters until the fugly French came in the 19th century.