Aside from many original inventions, the
Chinese
Chinese can refer to:
* Something related to China
* Chinese people, people of Chinese nationality, citizenship, and/or ethnicity
**''Zhonghua minzu'', the supra-ethnic concept of the Chinese nation
** List of ethnic groups in China, people of va ...
were also early original pioneers in the discovery of natural phenomena which can be found in the
human body
The human body is the structure of a Human, human being. It is composed of many different types of Cell (biology), cells that together create Tissue (biology), tissues and subsequently organ systems. They ensure homeostasis and the life, viabi ...
, the environment of the
world
In its most general sense, the term "world" refers to the totality of entities, to the whole of reality or to everything that is. The nature of the world has been conceptualized differently in different fields. Some conceptions see the worl ...
, and the immediate
Solar System
The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar S ...
. They also discovered many concepts in
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
. The list below contains discoveries which found their origins in
China
China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and ...
.
Discoveries
Ancient and imperial era
![Guardians of Day and Night, Han Dynasty](https://upload.wikimedia.org/wikipedia/commons/e/e8/Guardians_of_Day_and_Night%2C_Han_Dynasty.jpg)
*
Chinese remainder theorem
In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer ''n'' by several integers, then one can determine uniquely the remainder of the division of ''n'' by the product of thes ...
: The Chinese remainder theorem, including
simultaneous congruences in
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777â ...
, was first created in the 3rd century AD in the mathematical book ''
Sunzi Suanjing
''Sunzi Suanjing'' () was a mathematical treatise written during 3rd to 5th centuries AD which was listed as one of the Ten Computational Canons during the Tang dynasty. The specific identity of its author Sunzi (lit. "Master Sun") is still ...
'' posed the problem: "There is an unknown number of things, when divided by 3 it leaves 2, when divided by 5 it leaves 3, and when divided by 7 it leaves a remainder of 2. Find the number."
[Ho (1991), 516.] This method of calculation was used in calendrical mathematics by
Tang Dynasty
The Tang dynasty (, ; zh, t= ), or Tang Empire, was an Dynasties in Chinese history, imperial dynasty of China that ruled from 618 to 907 AD, with an Zhou dynasty (690–705), interregnum between 690 and 705. It was preceded by the Sui dyn ...
(618–907) mathematicians such as
Li Chunfeng
Li Chunfeng (; 602–670) was a Chinese mathematician, astronomer, historian, and politician who was born in today's Baoji, Shaanxi, during the Sui and Tang dynasties. He was first appointed to the Imperial Astronomy Bureau to help institute a ca ...
(602–670) and
Yi Xing
Yi Xing (, 683–727), born Zhang Sui (), was a Chinese astronomer, Buddhist monk, inventor, mathematician, mechanical engineer, and philosopher during the Tang dynasty. His astronomical celestial globe featured a liquid-driven escapement, the ...
(683–727) in order to determine the length of the "Great Epoch", the lapse of time between the conjunctions of the moon, sun, and Five Planets (
those discerned by the naked eye).
Thus, it was strongly associated with the
divination
Divination (from Latin ''divinare'', 'to foresee, to foretell, to predict, to prophesy') is the attempt to gain insight into a question or situation by way of an occultic, standardized process or ritual. Used in various forms throughout histor ...
methods of the ancient ''
Yijing
The ''I Ching'' or ''Yi Jing'' (, ), usually translated ''Book of Changes'' or ''Classic of Changes'', is an ancient Chinese divination text that is among the oldest of the Chinese classics. Originally a divination manual in the Western Zhou ...
''.
Its use was lost for centuries until
Qin Jiushao
Qin Jiushao (, ca. 1202–1261), courtesy name Daogu (é“å¤), was a Chinese mathematician, meteorologist, inventor, politician, and writer. He is credited for discovering Horner's method as well as inventing Tianchi basins, a type of rain gaug ...
(c. 1202–1261) revived it in his ''
Mathematical Treatise in Nine Sections
The ''Mathematical Treatise in Nine Sections'' () is a mathematical text written by Chinese Southern Song dynasty mathematician Qin Jiushao in the year 1247. The mathematical text has a wide range of topics and is taken from all aspects of the ...
'' of 1247, providing
constructive proof
In mathematics, a constructive proof is a method of mathematical proof, proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object. This is in contrast to a non-constructive proof (also ...
for it.
*
Circadian rhythm in humans: The observation of a circadian or diurnal process in humans is mentioned in Chinese medical texts dated to around the 13th century, including the ''Noon and Midnight Manual'' and the ''Mnemonic Rhyme to Aid in the Selection of Acu-points According to the Diurnal Cycle, the Day of the Month and the Season of the Year''.
*
Decimal fractions
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...
: decimal fractions were used in
Chinese mathematics
Mathematics in China emerged independently 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 ( base 2 and base 10), algebra, geomet ...
by the 1st century AD, as evidenced by ''
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 2nd century CE. This book is one of the earliest sur ...
'', while they appear in the works of
Arabic mathematics
Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta). Important progress was made, such as full ...
by the 11th century (however it is like it was independently developed) and in
European mathematics by the 12th century, although the decimal point was not used until the work of Francesco Pellos in 1492 and not clarified until the 1585 publication of
Flemish
Flemish (''Vlaams'') is a Low Franconian dialect cluster of the Dutch language. It is sometimes referred to as Flemish Dutch (), Belgian Dutch ( ), or Southern Dutch (). Flemish is native to Flanders, a historical region in northern Belgium; ...
mathematician
Simon Stevin
Simon Stevin (; 1548–1620), sometimes called Stevinus, was a Flemish mathematician, scientist and music theorist. He made various contributions in many areas of science and engineering, both theoretical and practical. He also translated vario ...
(1548–1620).
[Needham (1986), Volume 3, 89.]
*
Diabetes, recognition and treatment of: The ''
Huangdi Neijing
''Huangdi Neijing'' (), literally the ''Inner Canon of the Yellow Emperor'' or ''Esoteric Scripture of the Yellow Emperor'', is an ancient Chinese medical text or group of texts that has been treated as a fundamental doctrinal source for Chines ...
'' compiled by the 2nd century BC during the Han Dynasty identified diabetes as a disease suffered by those who had made an excessive habit of eating sweet and fatty foods, while the ''Old and New Tried and Tested Prescriptions'' written by the Tang Dynasty physician Zhen Quan (died 643) was the first known book to mention an excess of
sugar
Sugar is the generic name for sweet-tasting, soluble carbohydrates, many of which are used in food. Simple sugars, also called monosaccharides, include glucose, fructose, and galactose. Compound sugars, also called disaccharides or double ...
in the
urine
Urine is a liquid by-product of metabolism in humans and in many other animals. Urine flows from the kidneys through the ureters to the urinary bladder. Urination results in urine being excretion, excreted from the body through the urethra.
Cel ...
of diabetic patients.
[Medvei (1993), 49.]
![Bianzhong](https://upload.wikimedia.org/wikipedia/commons/8/80/Bianzhong.jpg)
*
Equal temperament
An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, wh ...
: During the
Han Dynasty
The Han dynasty (, ; ) was an imperial dynasty of China (202 BC – 9 AD, 25–220 AD), established by Liu Bang (Emperor Gao) and ruled by the House of Liu. The dynasty was preceded by the short-lived Qin dynasty (221–207 BC) and a warr ...
(202 BC–220 AD), the
music theorist
Music theory is the study of the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory". The first is the "rudiments", that are needed to understand music notation (ke ...
and mathematician
Jing Fang
Jing Fang (, 78–37 BC), born Li Fang (), courtesy name Junming (), was born in present-day æ±éƒ¡é “丘 ( Puyang, Henan) during the Han Dynasty (202 BC – 220 AD). He was a Chinese music theorist, mathematician and astrologer. Although ...
(78–37 BC) extended
the 12 tones found in the 2nd century BC ''
Huainanzi
The ''Huainanzi'' is an ancient Chinese text that consists of a collection of essays that resulted from a series of scholarly debates held at the court of Liu An, Prince of Huainan, sometime before 139. The ''Huainanzi'' blends Daoist, Confuci ...
'' to 60. While generating his 60-divisional tuning, he discovered that 53
just fifth
In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.
In classical music from Western culture, a fifth is the interval from the first to the last of five ...
s is approximate to 31
octave
In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...
s, calculating the difference at
; this was exactly the same value for
53 equal temperament
In music, 53 equal temperament, called 53 TET, 53 EDO, or 53 ET, is the tempered scale derived by dividing the octave into 53 equal steps (equal frequency ratios). Each step represents a frequency ratio of 2, or 22.6415 ...
calculated by the
German
German(s) may refer to:
* Germany (of or related to)
**Germania (historical use)
* Germans, citizens of Germany, people of German ancestry, or native speakers of the German language
** For citizens of Germany, see also German nationality law
**Ger ...
mathematician
Nicholas Mercator
Nicholas (Nikolaus) Mercator (c. 1620, Holstein – 1687, Versailles), also known by his German name Kauffmann, was a 17th-century mathematician.
He was born in Eutin, Schleswig-Holstein, Germany and educated at Rostock and Leyden after which he ...
(c. 1620–1687) as 3
53/2
84, a value known a
Mercator's Comma The
Ming Dynasty
The Ming dynasty (), officially the Great Ming, was an Dynasties in Chinese history, imperial dynasty of China, ruling from 1368 to 1644 following the collapse of the Mongol Empire, Mongol-led Yuan dynasty. The Ming dynasty was the last ort ...
(1368–1644) music theorist
Zhu Zaiyu
Zhu or ZHU may refer to:
*Zhu (surname), common Chinese surnames
*Zhu River, or Pearl River, in southern China
*Zhu (state), ancient Chinese state, later renamed Zou
*House of Zhu, the ruling house of the Ming dynasty in Chinese history
*Zhu (stri ...
(1536–1611) elaborated in three separate works beginning in 1584 the tuning system of equal temperament. In an unusual event in music theory's history, the
Flemish
Flemish (''Vlaams'') is a Low Franconian dialect cluster of the Dutch language. It is sometimes referred to as Flemish Dutch (), Belgian Dutch ( ), or Southern Dutch (). Flemish is native to Flanders, a historical region in northern Belgium; ...
mathematician
Simon Stevin
Simon Stevin (; 1548–1620), sometimes called Stevinus, was a Flemish mathematician, scientist and music theorist. He made various contributions in many areas of science and engineering, both theoretical and practical. He also translated vario ...
(1548–1620) discovered the mathematical formula for equal temperament at roughly the same time, yet he did not publish his work and it remained unknown until 1884 (whereas the ''Harmonie Universelle'' written in 1636 by
Marin Mersenne
Marin Mersenne, OM (also known as Marinus Mersennus or ''le Père'' Mersenne; ; 8 September 1588 – 1 September 1648) was a French polymath whose works touched a wide variety of fields. He is perhaps best known today among mathematicians for ...
is considered the first publication in Europe outlining equal temperament); therefore, it is debatable who discovered equal temperament first, Zhu or Stevin. In order to obtain
equal intervals, Zhu divided the octave (each octave with a ratio of 1:2, which can also be expressed as 1:2
12/12) into twelve equal
semitone
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically.
It is defined as the interval between two adjacent no ...
s while each length was divided by the 12th root of 2.
[Needham (1986), Volume 4, Part 1, 223.] He did not simply divide the string into twelve equal parts (i.e. 11/12, 10/12, 9/12, etc.) since this would give unequal temperament; instead, he altered the ratio of each semitone by an equal amount (i.e. 1:2
11/12, 1:2
10/12, 1:2
9/12, etc.) and determined the exact length of the string by dividing it by (same as 2
1/12).
*
Gaussian elimination
In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of operations performed on the corresponding matrix of coefficients. This method can also be used ...
: First published
in the West by
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...
(1777–1855) in 1826, the algorithm for
solving linear equations
Solution may refer to:
* Solution (chemistry), a mixture where one substance is dissolved in another
* Solution (equation), in mathematics
** Numerical solution, in numerical analysis, approximate solutions within specified error bounds
* Solutio ...
known as Gaussian elimination is named after this
Hanoverian mathematician, yet it was first expressed as the Array Rule in the Chinese ''
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 2nd century CE. This book is one of the earliest sur ...
'', written at most by 179 AD during the
Han Dynasty
The Han dynasty (, ; ) was an imperial dynasty of China (202 BC – 9 AD, 25–220 AD), established by Liu Bang (Emperor Gao) and ruled by the House of Liu. The dynasty was preceded by the short-lived Qin dynasty (221–207 BC) and a warr ...
(202 BC–220 AD) and commented on by the 3rd century mathematician
Liu Hui
Liu Hui () was a Chinese mathematician who published a commentary in 263 CE on ''Jiu Zhang Suan Shu (The Nine Chapters on the Mathematical Art).'' He was a descendant of the Marquis of Zixiang of the Eastern Han dynasty and lived in the state o ...
.
![Oxalis corniculata 1](https://upload.wikimedia.org/wikipedia/commons/2/21/Oxalis_corniculata_1.JPG)
*
Geomorphology
Geomorphology (from Ancient Greek: , ', "earth"; , ', "form"; and , ', "study") is the scientific study of the origin and evolution of topographic and bathymetric features created by physical, chemical or biological processes operating at or n ...
: In his ''
Dream Pool Essays
''The Dream Pool Essays'' (or ''Dream Torrent Essays'') was an extensive book written by the Chinese polymath and statesman Shen Kuo (1031–1095), published in 1088 during the Song dynasty (960–1279) of China. Shen compiled this encycloped ...
'' of 1088,
Shen Kuo
Shen Kuo (; 1031–1095) or Shen Gua, courtesy name Cunzhong (å˜ä¸) and pseudonym Mengqi (now usually given as Mengxi) Weng (夢溪ç¿),Yao (2003), 544. was a Chinese polymathic scientist and statesman of the Song dynasty (960–1279). Shen wa ...
(1031–1095) wrote about a landslide (near modern
Yan'an
Yan'an (; ), alternatively spelled as Yenan is a prefecture-level city in the Shaanbei region of Shaanxi province, China, bordering Shanxi to the east and Gansu to the west. It administers several counties, including Zhidan (formerly Bao'an ...
) where petrified
bamboo
Bamboos are a diverse group of evergreen perennial flowering plants making up the subfamily Bambusoideae of the grass family Poaceae. Giant bamboos are the largest members of the grass family. The origin of the word "bamboo" is uncertain, bu ...
s were discovered in a preserved state underground, in the dry northern climate zone of
Shanbei
Shaanbei () or Northern Shaanxi is the portion of China's Shaanxi province north of the Huanglong Mountain and the Meridian Ridge (the so-called "Guanzhong north mountains"), and is both a geographic as well as a cultural area.
It makes up the so ...
,
Shaanxi
Shaanxi (alternatively Shensi, see #Name, § Name) is a landlocked Provinces of China, province of China. Officially part of Northwest China, it borders the province-level divisions of Shanxi (NE, E), Henan (E), Hubei (SE), Chongqing (S), Sichu ...
; Shen reasoned that since bamboo was known only to grow in damp and humid conditions, the climate of this northern region must have been different in the very distant past, postulating that
climate change
In common usage, climate change describes global warming—the ongoing increase in global average temperature—and its effects on Earth's climate system. Climate change in a broader sense also includes previous long-term changes to E ...
occurred over time. Shen also advocated a hypothesis in line with
geomorphology
Geomorphology (from Ancient Greek: , ', "earth"; , ', "form"; and , ', "study") is the scientific study of the origin and evolution of topographic and bathymetric features created by physical, chemical or biological processes operating at or n ...
after he observed a stratum of marine fossils running in a horizontal span across a cliff of the
Taihang Mountains
The Taihang Mountains () are a Chinese mountain range running down the eastern edge of the Loess Plateau in Shanxi, Henan and Hebei provinces. The range extends over from north to south and has an average elevation of . The principal peak is ...
, leading him to believe that it was once the location of an ancient shoreline that had shifted hundreds of km (mi) east over time (due to deposition of silt and other factors).
*
Greatest Common Divisor
In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers ''x'', ''y'', the greatest common divisor of ''x'' and ''y'' is ...
: Rudolff gave in his text Kunstliche Rechnung, 1526 the rule for finding the greatest common divisor of two integers, which is to divide the larger by the smaller. If there is a remainder, divide the former divisor by this, and so on;. This is just the Mutual Subtraction Algorithm as found in the Rule for Reduction of Fractions, Chapter 1, of ''
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 2nd century CE. This book is one of the earliest sur ...
''
*
Grid reference
A projected coordinate system, also known as a projected coordinate reference system, a planar coordinate system, or grid reference system, is a type of spatial reference system that represents locations on the Earth using cartesian coordin ...
: Although professional map-making and use of the grid had
existed in China before, the Chinese cartographer and geographer
Pei Xiu
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 pa ...
of the Three Kingdoms period was the first to mention a plotted geometrical grid reference and graduated scale displayed on the surface of maps to gain greater accuracy in the estimated distance between different locations.
[Needham, Volume 3, 106–107.][Needham, Volume 3, 538–540.] Historian Howard Nelson asserts that there is ample written evidence that Pei Xiu derived the idea of the grid reference from the map of
Zhang Heng
Zhang Heng (; AD 78–139), formerly romanized as Chang Heng, was a Chinese polymathic scientist and statesman who lived during the Han dynasty. Educated in the capital cities of Luoyang and Chang'an, he achieved success as an astronomer, ma ...
(78–139 CE), a polymath inventor and statesman of the Eastern Han dynasty.
*
Irrational Numbers
In mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integ ...
: Although irrational numbers were first discovered by the Pythagorean Hippasus, the ancient Chinese never had the philosophical difficulties that the ancient Greeks had with irrational numbers such as the square root of 2. Simon Stevin (1548-1620) considered irrational numbers are numbers that can be continuously approximated by rationals. Li Hui in his comments on the Nine Chapters of Mathematical Art show he had the same understanding of irrationals. As early as the third century Liu knew how to get an approximation to an irrational with any required precision when extracting a square root, based on his comment on 'the Rule for Extracting the Square Root', and his comment on 'the Rule for Extracting the Cube Root'. The ancient Chinese did not differentiate between rational and irrational numbers, and simply calculated irrational numbers to the required degree of precision.
*
Jia Xian triangle: This triangle was the same as Pascal's Triangle, discovered by
Jia Xian
Jia Xian (; ca. 1010–1070) was a Chinese mathematician from Kaifeng of the Song dynasty.
Biography
According to the history of the Song dynasty, Jia was a palace eunuch of the Left Duty Group. He studied under the mathematician Chu Yan, and ...
in the first half of the 11th century, about six centuries before
Pascal
Pascal, Pascal's or PASCAL may refer to:
People and fictional characters
* Pascal (given name), including a list of people with the name
* Pascal (surname), including a list of people and fictional characters with the name
** Blaise Pascal, Fren ...
. Jia Xian used it as a tool for extracting
square
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length adj ...
and
cubic root
In mathematics, a cube root of a number is a number such that . All nonzero real numbers, have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. Fo ...
s. The original book by Jia Xian titled ''Shi Suo Suan Shu'' was lost; however, Jia's method was expounded in detail by
Yang Hui
Yang Hui (, ca. 1238–1298), courtesy name Qianguang (), was a Chinese mathematician and writer during the Song dynasty. Originally, from Qiantang (modern Hangzhou, Zhejiang), Yang worked on magic squares, magic circles and the binomial theor ...
, who explicitly acknowledged his source: "My method of finding square and cubic roots was based on the Jia Xian method in ''Shi Suo Suan Shu''." A page from the Yongle Encyclopedia preserved this historic fact.
![Gandhii looking after Sanskrit scholar Parchure Shastri, who was a leper patient](https://upload.wikimedia.org/wikipedia/commons/0/02/Gandhii_looking_after_Sanskrit_scholar_Parchure_Shastri%2C_who_was_a_leper_patient.jpg)
*
Leprosy, first description of its symptoms: The
''Feng zhen shi'' å°è¨ºå¼ (''Models for sealing and investigating''), written between 266 and 246 BC in the
State of Qin
Qin () was an ancient Chinese state during the Zhou dynasty. Traditionally dated to 897 BC, it took its origin in a reconquest of western lands previously lost to the Rong; its position at the western edge of Chinese civilization permitted ex ...
during the
Warring States period
The Warring States period () was an era in History of China#Ancient China, ancient Chinese history characterized by warfare, as well as bureaucratic and military reforms and consolidation. It followed the Spring and Autumn period and concluded ...
(403–221 BC), is the earliest known text which describes the symptoms of leprosy, termed under the generic word ''li'' 癘 (for skin disorders).
[McLeod & Yates (1981), 152–153 & footnote 147.] This text mentioned the destruction of the
nasal septum
The nasal septum () separates the left and right airways of the Human nose, nasal cavity, dividing the two nostrils.
It is Depression (kinesiology), depressed by the depressor septi nasi muscle.
Structure
The fleshy external end of the nasal ...
in those suffering from leprosy (an observation that would not be made outside of China until the writings of
Avicenna
Ibn Sina ( fa, ابن سینا; 980 – June 1037 CE), commonly known in the West as Avicenna (), was a Persian polymath who is regarded as one of the most significant physicians, astronomers, philosophers, and writers of the Islamic G ...
in the 11th century), and according to Katrina McLeod and Robin Yates it also stated lepers suffered from "swelling of the eyebrows, loss of hair, absorption of nasal cartilage, affliction of knees and elbows, difficult and hoarse respiration, as well as
anaesthesia
Anesthesia is a state of controlled, temporary loss of sensation or awareness that is induced for medical or veterinary purposes. It may include some or all of analgesia (relief from or prevention of pain), paralysis (muscle relaxation), am ...
."
Leprosy was not described
in the West until the writings of the
Roman
Roman or Romans most often refers to:
*Rome, the capital city of Italy
*Ancient Rome, Roman civilization from 8th century BC to 5th century AD
*Roman people, the people of ancient Rome
*''Epistle to the Romans'', shortened to ''Romans'', a letter ...
authors
Aulus Cornelius Celsus
Aulus Cornelius Celsus ( 25 BC 50 AD) was a Roman encyclopaedist, known for his extant medical work, ''De Medicina'', which is believed to be the only surviving section of a much larger encyclopedia. The ''De Medicina'' is a primary source on d ...
(25 BC – 37 AD) and
Pliny the Elder
Gaius Plinius Secundus (AD 23/2479), called Pliny the Elder (), was a Roman author, naturalist and natural philosopher, and naval and army commander of the early Roman Empire, and a friend of the emperor Vespasian. He wrote the encyclopedic '' ...
(23–79 AD).
Although it is alleged that the Indian ''
Sushruta Samhita
The ''Sushruta Samhita'' (सà¥à¤¶à¥à¤°à¥à¤¤à¤¸à¤‚हिता, IAST: ''SuÅ›rutasaṃhitÄ'', literally "SuÅ›ruta's Compendium") is an ancient Sanskrit text on medicine and surgery, and one of the most important such treatises on this subj ...
'', which describes leprosy, is dated to the 6th century BC,
India
India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...
's earliest written script (besides the then long extinct
Indus script
The Indus script, also known as the Harappan script, is a corpus of symbols produced by the Indus Valley Civilisation. Most inscriptions containing these symbols are extremely short, making it difficult to judge whether or not they constituted ...
)—the
BrÄhmÄ« script
Brahmi (; ; ISO: ''BrÄhmÄ«'') is a writing system of ancient South Asia. "Until the late nineteenth century, the script of the AÅ›okan (non-Kharosthi) inscriptions and its immediate derivatives was referred to by various names such as 'lath' o ...
—is thought to have been created no earlier than the 3rd century BC.
![Yuan dynasty iron magic square](https://upload.wikimedia.org/wikipedia/commons/2/2d/Yuan_dynasty_iron_magic_square.jpg)
*
Li Shanlan identity In mathematics, in combinatorics, the Li Shanlan identity (also called Li Shanlan's summation formula) is a certain combinatorial identity attributed to the nineteenth century Chinese mathematician Li Shanlan. Since Li Shanlan is also known as Li R ...
: discovered by the mathematician
Li Shanlan
Li Shanlan (æŽå–„è˜, courtesy name: Renshu 壬å”, art name: Qiuren 秋紉) (1810 – 1882) was a Chinese mathematician of the Qing Dynasty.
A native of Haining, Zhejiang, he was fascinated by mathematics since childhood, beginning with the '' ...
in 1867.
*
Liu Hui's π algorithm
Liu Hui's algorithm was invented by Liu Hui (fl. 3rd century), a mathematician of the state of Cao Wei. Before his time, the ratio of the circumference of a circle to its diameter was often taken experimentally as three in China, while Zhang H ...
: Liu Hui's π algorithm was invented by
Liu Hui
Liu Hui () was a Chinese mathematician who published a commentary in 263 CE on ''Jiu Zhang Suan Shu (The Nine Chapters on the Mathematical Art).'' He was a descendant of the Marquis of Zixiang of the Eastern Han dynasty and lived in the state o ...
(fl. 3rd century), a mathematician of
Wei Kingdom.
*
Magic squares
In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number o ...
: The earliest magic square is the
Lo Shu square
The Luoshu (pinyin), Lo Shu ( Wade-Giles), or Nine Halls Diagram is an ancient Chinese diagram and named for the Luo River near Luoyang, Henan. The Luoshu appears in myths concerning the invention of writing by Cangjie and other culture heroes. ...
, dating to 4th century BCE China. The square was viewed as mystical, and according to Chinese mythology, "was first seen by
Emperor Yu."
*
Map scaling: The foundations for quantitative map scaling goes back to ancient China with textual evidence that the idea of map scaling was understood by the second century BC. Ancient Chinese surveyors and cartographers had ample technical resources used to produce maps such as
counting rods
Counting rods () are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient East Asia. They are placed either horizontally or vertically to represent any integer or rational number.
The written fo ...
,
carpenter's square
The steel square is a tool used in carpentry. Carpenters use various tools to lay out structures that are square (that is, built at accurately measured right angles), many of which are made of steel, but the name ''steel square'' refers to a spec ...
's,
plumb lines,
compasses
A compass, more accurately known as a pair of compasses, is a technical drawing instrument that can be used for inscribing circles or arcs. As dividers, it can also be used as a tool to mark out distances, in particular, on maps. Compasses c ...
for drawing circles, and sighting tubes for measuring inclination. Reference frames postulating a nascent coordinate system for identifying locations were hinted by ancient Chinese astronomers that divided the sky into various sectors or lunar lodges.
The Chinese cartographer and geographer
Pei Xiu
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 pa ...
of the Three Kingdoms period created a set of large-area maps that were drawn to scale. He produced a set of principles that stressed the importance of consistent scaling, directional measurements, and adjustments in land measurements in the terrain that was being mapped.
*
Negative numbers, symbols for and use of: in 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 2nd century CE. This book is one of the earliest sur ...
'' compiled during the
Han Dynasty
The Han dynasty (, ; ) was an imperial dynasty of China (202 BC – 9 AD, 25–220 AD), established by Liu Bang (Emperor Gao) and ruled by the House of Liu. The dynasty was preceded by the short-lived Qin dynasty (221–207 BC) and a warr ...
(202 BC–220 AD) by 179 AD and commented on by
Liu Hui
Liu Hui () was a Chinese mathematician who published a commentary in 263 CE on ''Jiu Zhang Suan Shu (The Nine Chapters on the Mathematical Art).'' He was a descendant of the Marquis of Zixiang of the Eastern Han dynasty and lived in the state o ...
(fl. 3rd century) in 263,
negative numbers appear as rod numerals in a slanted position.
[Needham (1986), Volume 3, 91.] Negative numbers represented as black rods and positive numbers as red rods in the Chinese
counting rods
Counting rods () are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient East Asia. They are placed either horizontally or vertically to represent any integer or rational number.
The written fo ...
system perhaps existed as far back as the 2nd century BC during the
Western Han
The Han dynasty (, ; ) was an Dynasties in Chinese history, imperial dynasty of China (202 BC – 9 AD, 25–220 AD), established by Emperor Gaozu of Han, Liu Bang (Emperor Gao) and ruled by the House of Liu. The dynasty was preceded by th ...
, while it was an established practice in Chinese algebra during the
Song dynasty
The Song dynasty (; ; 960–1279) was an imperial dynasty of China that began in 960 and lasted until 1279. The dynasty was founded by Emperor Taizu of Song following his usurpation of the throne of the Later Zhou. The Song conquered the rest ...
(960-1279 AD).
[Needham (1986), Volume 3, 90-91.] Negative numbers denoted by a "+" sign also appear in the ancient
Bakhshali manuscript of
India
India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...
, yet scholars disagree as to when it was compiled, giving a collective range of 200 to 600 AD.
[Teresi (2002), 65–66.] Negative numbers were known in India certainly by about 630 AD, when the mathematician
Brahmagupta
Brahmagupta ( – ) was an Indian mathematician and astronomer. He is the author of two early works on mathematics and astronomy: the ''BrÄhmasphuá¹asiddhÄnta'' (BSS, "correctly established doctrine of Brahma", dated 628), a theoretical trea ...
(598–668) used them.
[Needham (1986), Volume 3, 90.] Negative numbers were first used in Europe by the
Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group.
*Greek language, a branch of the Indo-European language family.
**Proto-Greek language, the assumed last common ancestor ...
mathematician
Diophantus
Diophantus of Alexandria ( grc, Διόφαντος ὠἈλεξανδÏεÏÏ‚; born probably sometime between AD 200 and 214; died around the age of 84, probably sometime between AD 284 and 298) was an Alexandrian mathematician, who was the aut ...
(fl. 3rd century) in about 275 AD, yet were considered an absurd concept in
Western
Western may refer to:
Places
*Western, Nebraska, a village in the US
*Western, New York, a town in the US
*Western Creek, Tasmania, a locality in Australia
*Western Junction, Tasmania, a locality in Australia
*Western world, countries that id ...
mathematics until
''The Great Art'' written in 1545 by the
Italian
Italian(s) may refer to:
* Anything of, from, or related to the people of Italy over the centuries
** Italians, an ethnic group or simply a citizen of the Italian Republic or Italian Kingdom
** Italian language, a Romance language
*** Regional Ita ...
mathematician
Girolamo Cardano
Gerolamo Cardano (; also Girolamo or Geronimo; french: link=no, Jérôme Cardan; la, Hieronymus Cardanus; 24 September 1501– 21 September 1576) was an Italian polymath, whose interests and proficiencies ranged through those of mathematician, ...
(1501–1576).
*
Pi calculated as : The ancient
Egyptians
Egyptians ( arz, المَصرÙÙŠÙون, translit=al-Maá¹£riyyÅ«n, ; arz, المَصرÙÙŠÙين, translit=al-Maá¹£riyyÄ«n, ; cop, ⲣⲉⲙⲛ̀â²â²â²™â²“, remenkhÄ“mi) are an ethnic group native to the Nile, Nile Valley in Egypt. Egyptian ...
,
Babylonians
Babylonia (; Akkadian: , ''mÄt AkkadÄ«'') was an ancient Akkadian-speaking state and cultural area based in the city of Babylon in central-southern Mesopotamia (present-day Iraq and parts of Syria). It emerged as an Amorite-ruled state c. ...
,
Indians, and
Greeks
The Greeks or Hellenes (; el, Έλληνες, ''Éllines'' ) are an ethnic group and nation indigenous to the Eastern Mediterranean and the Black Sea regions, namely Greece, Cyprus, Albania, Italy, Turkey, Egypt, and, to a lesser extent, oth ...
had
long made approximations for π by the time the Chinese mathematician and astronomer
Liu Xin (c. 46 BC–23 AD) improved the old Chinese approximation of simply 3 as Ï€ to 3.1547 as Ï€ (with evidence on vessels dating to the
Wang Mang
Wang Mang () (c. 45 – 6 October 23 CE), courtesy name Jujun (), was the founder and the only Emperor of China, emperor of the short-lived Chinese Xin dynasty. He was originally an official and consort kin of the Han dynasty and later ...
reign period, 9–23 AD, of other approximations of 3.1590, 3.1497, and 3.1679).
Next,
Zhang Heng
Zhang Heng (; AD 78–139), formerly romanized as Chang Heng, was a Chinese polymathic scientist and statesman who lived during the Han dynasty. Educated in the capital cities of Luoyang and Chang'an, he achieved success as an astronomer, ma ...
(78–139 AD) made two approximations for Ï€, by proportioning the celestial circle to the diameter of the earth as
= 3.1724 and using (after a long algorithm) the
square root
In mathematics, a square root of a number is a number such that ; in other words, a number whose ''square'' (the result of multiplying the number by itself, or  ⋅ ) is . For example, 4 and −4 are square roots of 16, because .
E ...
of 10, or 3.162.
[Berggren, Borwein & Borwein (2004), 27] In his commentary on the
Han Dynasty
The Han dynasty (, ; ) was an imperial dynasty of China (202 BC – 9 AD, 25–220 AD), established by Liu Bang (Emperor Gao) and ruled by the House of Liu. The dynasty was preceded by the short-lived Qin dynasty (221–207 BC) and a warr ...
mathematical work ''
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 2nd century CE. This book is one of the earliest sur ...
'',
Liu Hui
Liu Hui () was a Chinese mathematician who published a commentary in 263 CE on ''Jiu Zhang Suan Shu (The Nine Chapters on the Mathematical Art).'' He was a descendant of the Marquis of Zixiang of the Eastern Han dynasty and lived in the state o ...
(fl. 3rd century)
used various algorithms to render multiple approximations for pi at 3.142704, 3.1428, and 3.14159. Finally, the mathematician and astronomer
Zu Chongzhi
Zu Chongzhi (; 429–500 AD), courtesy name Wenyuan (), was a Chinese astronomer, mathematician, politician, inventor, and writer during the Liu Song and Southern Qi dynasties. He was most notable for calculating pi as between 3.1415926 and 3. ...
(429–500) approximated pi to an even greater degree of accuracy, rendering it
, a value known in Chinese as
Milü ("detailed ratio"). This was the best
rational
Rationality is the quality of being guided by or based on reasons. In this regard, a person acts rationally if they have a good reason for what they do or a belief is rational if it is based on strong evidence. This quality can apply to an abili ...
approximation for pi with a
denominator
A fraction (from la, fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight ...
of up to four digits; the next rational number is
, which is the
best rational approximation
In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer pa ...
. Zu ultimately determined the value for π to be between 3.1415926 and 3.1415927. Zu's approximation was the most accurate in the world, and would not be achieved elsewhere for another millennium, until
Madhava of Sangamagrama
IriññÄttappiḷḷi MÄdhavan known as MÄdhava of SangamagrÄma () was an Indian mathematician and astronomer from the town believed to be present-day Kallettumkara, Aloor Panchayath, Irinjalakuda in Thrissur District, Kerala, India. He is ...
and
JamshÄ«d al-KÄshÄ«
GhiyÄth al-DÄ«n JamshÄ«d MasÊ¿Å«d al-KÄshÄ« (or al-KÄshÄnÄ«) ( fa, غیاث الدین جمشید کاشانی ''GhiyÄs-ud-dÄ«n JamshÄ«d KÄshÄnÄ«'') (c. 1380 Kashan, Iran – 22 June 1429 Samarkand, Transoxania) was a Persian astronomer a ...
in the early 15th century.
![B05n](https://upload.wikimedia.org/wikipedia/commons/f/f4/B05n.jpg)
*
True north, concept of: The
Song Dynasty
The Song dynasty (; ; 960–1279) was an imperial dynasty of China that began in 960 and lasted until 1279. The dynasty was founded by Emperor Taizu of Song following his usurpation of the throne of the Later Zhou. The Song conquered the rest ...
(960–1279) official
Shen Kuo
Shen Kuo (; 1031–1095) or Shen Gua, courtesy name Cunzhong (å˜ä¸) and pseudonym Mengqi (now usually given as Mengxi) Weng (夢溪ç¿),Yao (2003), 544. was a Chinese polymathic scientist and statesman of the Song dynasty (960–1279). Shen wa ...
(1031–1095), alongside his colleague
Wei Pu Wei Pu (; Wade-Giles: Wei P'u) was a Chinese astronomer and politician of the Song Dynasty (960-1279 AD). He was born a commoner, but eventually rose to prominence as an astronomer working for the imperial court at the capital of Kaifeng.Sivin, III ...
, improved the orifice width of the sighting tube to make nightly accurate records of the paths of the moon, stars, and planets in the night sky, for a continuum of five years. By doing so, Shen fixed the outdated position of the
pole star
A pole star or polar star is a star, preferably bright, nearly aligned with the axis of a rotating astronomical body.
Currently, Earth's pole stars are Polaris (Alpha Ursae Minoris), a bright magnitude-2 star aligned approximately with its ...
, which had shifted over the centuries since the time
Zu Geng (fl. 5th century) had plotted it; this was due to the
precession of the Earth's rotational axis.
[Sivin (1995), III, 22.][Needham (1986), Volume 3, 278.] When making the first known experiments with a magnetic
compass
A compass is a device that shows the cardinal directions used for navigation and geographic orientation. It commonly consists of a magnetized needle or other element, such as a compass card or compass rose, which can pivot to align itself with ...
, Shen Kuo wrote that the needle always pointed slightly east rather than due south, an angle he measured which is now known as
magnetic declination
Magnetic declination, or magnetic variation, is the angle on the horizontal plane between magnetic north (the direction the north end of a magnetized compass needle points, corresponding to the direction of the Earth's magnetic field lines) and ...
, and wrote that the compass needle in fact pointed towards the
magnetic north pole
The north magnetic pole, also known as the magnetic north pole, is a point on the surface of Earth's Northern Hemisphere at which the planet's magnetic field points vertically downward (in other words, if a magnetic compass needle is allowed t ...
instead of true north (indicated by the current pole star); this was a critical step in the history of accurate
navigation
Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navigation, ...
with a compass.
[Sivin (1995), III, 21–22.]
Modern era
*
Arteminisinin, anti-malarial treatment: The
antimalarial
Antimalarial medications or simply antimalarials are a type of antiparasitic chemical agent, often naturally derived, that can be used to treat or to prevent malaria, in the latter case, most often aiming at two susceptible target groups, young c ...
drug of compound
artemisinin
Artemisinin () and its semisynthetic derivatives are a group of drugs used in the treatment of malaria due to ''Plasmodium falciparum''. It was discovered in 1972 by Tu Youyou, who shared the 2015 Nobel Prize in Physiology or Medicine for her dis ...
found in ''
Artemisia annua
''Artemisia annua'', also known as sweet wormwood, sweet annie, sweet sagewort, annual mugwort or annual wormwood (), is a common type of wormwood native to temperate Asia, but naturalized in many countries including scattered parts of North Am ...
'', the latter being a plant long used in
traditional Chinese medicine
Traditional Chinese medicine (TCM) is an alternative medical practice drawn from traditional medicine in China. It has been described as "fraught with pseudoscience", with the majority of its treatments having no logical mechanism of action ...
, was discovered in 1972 by
Chinese scientists in the People's Republic led by
Tu Youyou
Tu Youyou (; born 30 December 1930) is a Chinese pharmaceutical chemist and malariologist. She discovered artemisinin (also known as , ) and dihydroartemisinin, used to treat malaria, a breakthrough in twentieth-century tropical medicine, sav ...
and has been used to treat multi-drug resistant strains of ''
Plasmodium falciparum
''Plasmodium falciparum'' is a Unicellular organism, unicellular protozoan parasite of humans, and the deadliest species of ''Plasmodium'' that causes malaria in humans. The parasite is transmitted through the bite of a female ''Anopheles'' mosqu ...
'' malaria. Artemisinin remains the most effective treatment for malaria today and has saved millions of lives and is yielded one of the greatest drug discoveries in modern medicine.
*
Chen's theorem
In number theory, Chen's theorem states that every sufficiently large parity (mathematics), even number can be written as the sum of either two prime number, primes, or a prime and a semiprime (the product of two primes).
History
The theorem wa ...
: Chen's theorem states that every sufficiently large even number can be written as the sum of either two
primes
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
, or a prime and a
semiprime
In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers.
Because there are infinitely many prime nu ...
, and was first proven by
Chen Jingrun
Chen Jingrun (; 22 May 1933 – 19 March 1996), also known as Jing-Run Chen, was a Chinese mathematician who made significant contributions to number theory, including Chen's theorem and the Chen prime.
Life and career
Chen was the third son in ...
in 1966, with further details of the
proof
Proof most often refers to:
* Proof (truth), argument or sufficient evidence for the truth of a proposition
* Alcohol proof, a measure of an alcoholic drink's strength
Proof may also refer to:
Mathematics and formal logic
* Formal proof, a con ...
in 1973.
*
Chen prime
A prime number ''p'' is called a Chen prime if ''p'' + 2 is either a prime or a product of two primes (also called a semiprime). The even number 2''p'' + 2 therefore satisfies Chen's theorem.
The Chen primes are named after Chen Jin ...
: A
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
''p'' is called a Chen prime if ''p'' + 2 is either a prime or a
product of two primes (also called a semiprime). The
even number
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is a multiple of two, and odd if it is not.. For example, −4, 0, 82 are even because
\begin
-2 \cdot 2 &= -4 \\
0 \cdot 2 &= 0 \\
41 ...
2''p'' + 2 therefore satisfies
Chen's theorem
In number theory, Chen's theorem states that every sufficiently large parity (mathematics), even number can be written as the sum of either two prime number, primes, or a prime and a semiprime (the product of two primes).
History
The theorem wa ...
. The Chen primes are named after
Chen Jingrun
Chen Jingrun (; 22 May 1933 – 19 March 1996), also known as Jing-Run Chen, was a Chinese mathematician who made significant contributions to number theory, including Chen's theorem and the Chen prime.
Life and career
Chen was the third son in ...
, who proved in 1966 that there are
infinitely
Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol .
Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions amo ...
many such primes. This result would also follow from the truth of the
twin prime conjecture
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin pr ...
.
*
Cheng's eigenvalue comparison theorem
In Riemannian geometry, Cheng's eigenvalue comparison theorem states in general terms that when a domain is large, the first Dirichlet eigenvalue of its Laplace–Beltrami operator is small. This general characterization is not precise, in part be ...
: Cheng's theorem was introduced in 1975 by Hong Kong mathematician
Shiu-Yuen Cheng
Shiu-Yuen Cheng (é„ç´¹é ) is a Hong Kong mathematician. He is currently the Chair Professor of Mathematics at the Hong Kong University of Science and Technology. Cheng received his Ph.D. in 1974, under the supervision of Shiing-Shen Chern, from ...
. It states in general terms that when a domain is large, the first
Dirichlet eigenvalue In mathematics, the Dirichlet eigenvalues are the fundamental modes of vibration of an idealized drum with a given shape. The problem of whether one can hear the shape of a drum is: given the Dirichlet eigenvalues, what features of the shape of t ...
of its
Laplace–Beltrami operator
In differential geometry, the Laplace–Beltrami operator is a generalization of the Laplace operator to functions defined on submanifolds in Euclidean space and, even more generally, on Riemannian and pseudo-Riemannian manifolds. It is named af ...
is small. This general characterization is not precise, in part because the notion of "size" of the domain must also account for its
curvature
In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane.
For curves, the canonic ...
.
*
Chern class
In mathematics, in particular in algebraic topology, differential geometry and algebraic geometry, the Chern classes are characteristic classes associated with complex vector bundles. They have since found applications in physics, Calabi–Yau ma ...
: Chern classes are
characteristic classes
In mathematics, a characteristic class is a way of associating to each principal bundle of ''X'' a cohomology class of ''X''. The cohomology class measures the extent the bundle is "twisted" and whether it possesses sections. Characteristic classe ...
in mathematics first introduced by
Shiing-Shen Chern
Shiing-Shen Chern (; , ; October 28, 1911 – December 3, 2004) was a Chinese-American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geome ...
in 1946.
*
Chow's moving lemma In algebraic geometry, Chow's moving lemma, proved by , states: given algebraic cycles ''Y'', ''Z'' on a nonsingular quasi-projective variety ''X'', there is another algebraic cycle ''Z' '' on ''X'' such that ''Z' '' is rationally equivalent to '' ...
: In algebraic geometry, Chow's moving lemma, named after
Wei-Liang Chow
Chow Wei-Liang (; October 1, 1911, Shanghai – August 10, 1995, Baltimore) was a Chinese mathematician and stamp collector born in Shanghai, known for his work in algebraic geometry.
Biography
Chow was a student in the US, graduating from the ...
, states: given
algebraic cycles In mathematics, an algebraic cycle on an algebraic variety ''V'' is a formal linear combination of subvarieties of ''V''. These are the part of the algebraic topology of ''V'' that is directly accessible by algebraic methods. Understanding the alg ...
''Y'', ''Z'' on a nonsingular quasi-projective variety ''X'', there is another algebraic cycle ''Z' '' on ''X'' such that ''Z' '' is
rationally equivalent In algebraic geometry, a branch of mathematics, an adequate equivalence relation is an equivalence relation on algebraic cycles of smooth projective varieties used to obtain a well-working theory of such cycles, and in particular, well-defined inte ...
to ''Z'' and ''Y'' and ''Z' '' intersect properly. The lemma is one of key ingredients in developing the
intersection theory
In mathematics, intersection theory is one of the main branches of algebraic geometry, where it gives information about the intersection of two subvarieties of a given variety. The theory for varieties is older, with roots in Bézout's theore ...
, as it is used to show the uniqueness of the theory.
* Culturing
Chlamydia trachomatis
''Chlamydia trachomatis'' (), commonly known as chlamydia, is a bacterium that causes chlamydia, which can manifest in various ways, including: trachoma, lymphogranuloma venereum, nongonococcal urethritis, cervicitis, salpingitis, pelvic inflamma ...
bacteria: Chlamydia trachomatis agent was first cultured in the yolk sacs of eggs by Chinese scientists in 1957
*
Feathered theropods: The first feathered dinosaur outside of
Avialae
Avialae ("bird wings") is a clade containing the only living dinosaurs, the birds. It is usually defined as all theropod dinosaurs more closely related to birds (Aves) than to deinonychosaurs, though alternative definitions are occasionally used ...
, ''
Sinosauropteryx
''Sinosauropteryx'' (meaning "Chinese reptilian wing", ) is a compsognathid dinosaur. Described in 1996, it was the first dinosaur taxon outside of Avialae (birds and their immediate relatives) to be found with evidence of feathers. It was covere ...
'', meaning "Chinese reptilian wing," was discovered in the
Yixian Formation
The Yixian Formation (; formerly transcribed as Yihsien Formation) is a geological formation in Jinzhou, Liaoning, People's Republic of China, that spans the late Barremian and early Aptian stages of the Early Cretaceous. It is known for its ex ...
by Chinese paleontologists in 1996.
The discovery is seen as evidence that dinosaurs
originated from birds, a theory proposed and supported decades earlier by paleontologists like
Gerhard Heilmann
Gerhard Heilmann (later sometimes spelt "Heilman") (25 June 1859 – 26 March 1946) was a Danish artist and paleontologist who created artistic depictions of ''Archaeopteryx'', ''Proavis'' and other early bird relatives apart from writing the 1926 ...
and
John Ostrom
John Harold Ostrom (February 18, 1928 – July 16, 2005) was an American paleontologist who revolutionized modern understanding of dinosaurs in the 1960s.
As first proposed by Thomas Henry Huxley in the 1860s, Ostrom showed that dinosaurs were ...
, but "no true dinosaur had been found exhibiting down or feathers until the Chinese specimen came to light."
The dinosaur was covered in what are dubbed 'protofeathers' and considered to be
homologous with the more advanced feathers of birds,
although some scientists disagree with this assessment.
*
Finite element method
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat ...
: In
numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...
, the finite element method is a technique for finding approximate solutions to systems of
partial differential equations
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function.
The function is often thought of as an "unknown" to be solved for, similarly to ...
. The FEM was developed in the West by
Alexander Hrennikoff
Alexander Pavlovich Hrennikoff (russian: ÐлекÑандр Павлович Хренников; 11 November 1896 — 31 December 1984) was a Russian-Canadians, Canadian structural engineer, a founder of the Finite Element Method.
Biography
Alexa ...
and
Richard Courant
Richard Courant (January 8, 1888 – January 27, 1972) was a German American mathematician. He is best known by the general public for the book '' What is Mathematics?'', co-written with Herbert Robbins. His research focused on the areas of real ...
, and independently in China by
Feng Kang.
*
Grunwald–Wang theorem
In algebraic number theory, the Grunwald–Wang theorem is a local-global principle stating that—except in some precisely defined cases—an element ''x'' in a number field ''K'' is an ''n''th power in ''K'' if it is an ''n''th power in the comp ...
: In
algebraic number theory
Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic ob ...
, the Grunwald–Wang theorem states that—except in some precisely defined cases—an element ''x'' in a
number field
In mathematics, an algebraic number field (or simply number field) is an extension field K of the field of rational numbers such that the field extension K / \mathbb has finite degree (and hence is an algebraic field extension).
Thus K is a f ...
''K'' is an ''n''th power in ''K'' if it is an ''n''th power in the
completion for
almost all
In mathematics, the term "almost all" means "all but a negligible amount". More precisely, if X is a set, "almost all elements of X" means "all elements of X but those in a negligible subset of X". The meaning of "negligible" depends on the math ...
(i.e. all but finitely many) primes
of ''K''. For example, a
rational number
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all ration ...
is a square of a rational number if it is a square of a
''p''-adic number for almost all primes ''p''. The Grunwald–Wang theorem is an example of a
local-global principle In mathematics, Helmut Hasse's local–global principle, also known as the Hasse principle, is the idea that one can find an integer solution to an equation by using the Chinese remainder theorem to piece together solutions modulo powers of each ...
. It was introduced by , but there was a mistake in this original version that was found and corrected by .
*
Hua's identity
In algebra, Hua's identity named after Hua Luogeng, states that for any elements ''a'', ''b'' in a division ring,
a - \left(a^ + \left(b^ - a\right)^\right)^ = aba
whenever ab \ne 0, 1. Replacing b with -b^ gives another equivalent form of the ide ...
: In algebra, Hua's identity states that for any elements ''a'', ''b'' in a
division ring
In algebra, a division ring, also called a skew field, is a nontrivial ring in which division by nonzero elements is defined. Specifically, it is a nontrivial ring in which every nonzero element has a multiplicative inverse, that is, an element us ...
, :
whenever
. Replacing
with
gives another equivalent form of the identity: :
*
Hua's lemma In mathematics, Hua's lemma, named for Hua Loo-keng, is an estimate for exponential sums.
It states that if ''P'' is an integral-valued polynomial In mathematics, an integer-valued polynomial (also known as a numerical polynomial) P(t) is a polyno ...
: In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, Hua's lemma, named for
Hua Loo-keng
Hua Luogeng or Hua Loo-Keng (; 12 November 1910 – 12 June 1985) was a Chinese mathematician and politician famous for his important contributions to number theory and for his role as the leader of mathematics research and education in the Peop ...
, is an estimate for
exponential sum
In mathematics, an exponential sum may be a finite Fourier series (i.e. a trigonometric polynomial), or other finite sum formed using the exponential function, usually expressed by means of the function
:e(x) = \exp(2\pi ix).\,
Therefore, a typic ...
s.
*
Heterosis in rice, three-line hybrid rice system: A team of agricultural scientists headed by
Yuan Longping
Yuan Longping (; September 7, 1930May 22, 2021) was a Chinese agronomist and member of the Chinese Academy of Engineering known for developing the first hybrid rice varieties in the 1970s, part of the Green Revolution in agriculture. For his ...
applied
heterosis
Heterosis, hybrid vigor, or outbreeding enhancement is the improved or increased function of any biological quality in a hybrid offspring. An offspring is heterotic if its traits are enhanced as a result of mixing the genetic contributions of ...
to rice, developing the three-line hybrid rice system in 1973. The innovation allowed for roughly 12,000 kg (26,450 lbs) of rice to be grown per hectare (10,000 m
2). Hybrid rice has proven to be greatly beneficial in areas where there is little arable land, and has been adopted by several Asian and African countries. Yuan won the 2004
Wolf Prize
The Wolf Prize is an international award granted in Israel, that has been presented most years since 1978 to living scientists and artists for ''"achievements in the interest of mankind and friendly relations among people ... irrespective of natio ...
in agriculture for his work.
*
Huang-Minglon modification: The Huang-Minglon modification, introduced by Chinese chemist
Huang Minlon
Huang Minlon, Huang-Minlon, or Huang Minglong (; 3 July 1898 – 1 July 1979) was a Chinese organic chemist and pharmaceutical scientist. Huang is considered a pioneer and founder of modern pharmaceutical industries in China.
Life
Huang was bor ...
, is a modification of the Wolff–Kishner reduction and involves heating the
carbonyl
In organic chemistry, a carbonyl group is a functional group composed of a carbon atom double-bonded to an oxygen atom: C=O. It is common to several classes of organic compounds, as part of many larger functional groups. A compound containing a ...
compound,
potassium hydroxide
Potassium hydroxide is an inorganic compound with the formula K OH, and is commonly called caustic potash.
Along with sodium hydroxide (NaOH), KOH is a prototypical strong base. It has many industrial and niche applications, most of which exp ...
, and
hydrazine
Hydrazine is an inorganic compound with the chemical formula . It is a simple pnictogen hydride, and is a colourless flammable liquid with an ammonia-like odour. Hydrazine is highly toxic unless handled in solution as, for example, hydrazine ...
hydrate together in
ethylene glycol
Ethylene glycol (IUPAC name: ethane-1,2-diol) is an organic compound (a vicinal diol) with the formula . It is mainly used for two purposes, as a raw material in the manufacture of polyester fibers and for antifreeze formulations. It is an odo ...
in a
one-pot reaction
In chemistry a one-pot synthesis is a strategy to improve the efficiency of a chemical reaction whereby a reactant is subjected to successive chemical reactions in just one reactor. This is much desired by chemists because avoiding a lengthy separ ...
.
*
Ky Fan norm
In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any \ m \times n\ matrix. It is related ...
s: The sum of the ''k'' largest singular values of ''M'' is a
matrix norm
In mathematics, a matrix norm is a vector norm in a vector space whose elements (vectors) are matrices (of given dimensions).
Preliminaries
Given a field K of either real or complex numbers, let K^ be the -vector space of matrices with m rows ...
, the
Ky Fan
Ky Fan (樊𰋀, , September 19, 1914 – March 22, 2010) was a Chinese-born American mathematician. He was a professor of mathematics at the University of California, Santa Barbara.
Biography
Fan was born in Hangzhou, the capital of Zhejian ...
''k''-norm of ''M''. The first of the Ky Fan norms, the Ky Fan 1-norm is the same as the
operator norm
In mathematics, the operator norm measures the "size" of certain linear operators by assigning each a real number called its . Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces.
Introdu ...
of ''M'' as a linear operator with respect to the Euclidean norms of ''K''
''m'' and ''K''
''n''. In other words, the Ky Fan 1-norm is the operator norm induced by the standard ''l''
2 Euclidean inner product.
*
Lee–Yang theorem: The Lee-Yang theorem in
statistical mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic be ...
was first proved for the
Ising model
The Ising model () (or Lenz-Ising model or Ising-Lenz model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent ...
by future Nobel laureates
Tsung-Dao Lee
Tsung-Dao Lee (; born November 24, 1926) is a Chinese-American physicist, known for his work on parity violation, the Lee–Yang theorem, particle physics, relativistic heavy ion (RHIC) physics, nontopological solitons, and soliton star ...
and
Chen Ning Yang
Yang Chen-Ning or Chen-Ning Yang (; born 1 October 1922), also known as C. N. Yang or by the English name Frank Yang, is a Chinese theoretical physicist who made significant contributions to statistical mechanics, integrable systems, gauge the ...
in 1952. The theorem states that if
partition functions
Partition may refer to:
Computing Hardware
* Disk partitioning, the division of a hard disk drive
* Memory partition, a subdivision of a computer's memory, usually for use by a single job
Software
* Partition (database), the division of a ...
of certain models in
statistical field theory
Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industria ...
with ferromagnetic interactions are considered as functions of an external field, then all zeros are purely imaginary, or on the unit circle after a change of variable.
*
Pu's inequality
In differential geometry, Pu's inequality, proved by Pao Ming Pu, relates the area of an arbitrary Riemannian surface homeomorphic to the real projective plane with the lengths of the closed curves contained in it.
Statement
A student of Charle ...
: In
differential geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...
, Pu's inequality is an inequality proved by
Pao Ming Pu Pao Ming Pu (the form of his name he used in Western languages, although the Wade-Giles transliteration would be Pu Baoming; ; August 1910 – February 22, 1988), was a mathematician born in Jintang County, Sichuan, China..
He was a student ...
for the
systole
Systole ( ) is the part of the cardiac cycle during which some chambers of the heart contract after refilling with blood. The term originates, via New Latin, from Ancient Greek (''sustolē''), from (''sustéllein'' 'to contract'; from ''sun ...
of an arbitrary
Riemannian metric
In differential geometry, a Riemannian manifold or Riemannian space , so called after the German mathematician Bernhard Riemann, is a real, smooth manifold ''M'' equipped with a positive-definite inner product ''g'p'' on the tangent space ''T ...
on the
real projective plane
In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface. It cannot be embedded in standard three-dimensional space without intersecting itself. It has bas ...
RP
2.
*
Siu's semicontinuity theorem: In
complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...
, the Siu semicontinuity theorem implies that the
Lelong number of a closed
positive current In mathematics, more particularly in complex geometry,
algebraic geometry and complex analysis, a positive current
is a positive (''n-p'',''n-p'')-form over an ''n''-dimensional complex manifold,
taking values in distributions.
For a formal defi ...
on a
complex manifold
In differential geometry and complex geometry, a complex manifold is a manifold with an atlas of charts to the open unit disc in \mathbb^n, such that the transition maps are holomorphic.
The term complex manifold is variously used to mean a com ...
is
semicontinuous. More precisely, the points where the Lelong number is at least some constant form a complex
subvariety
A subvariety (Latin: ''subvarietas'') in botanical nomenclature is a taxonomic rank. They are rarely used to classify organisms.
Plant taxonomy
Subvariety is ranked:
*below that of variety (''varietas'')
*above that of form (''forma'').
Subva ...
. This was conjectured by and proved by .
*
Sun's curious identity
In combinatorics, Sun's curious identity is the following identity involving binomial coefficients, first established by Zhi-Wei Sun in 2002:
:
(x+m+1)\sum_^m(-1)^i\dbinom\dbinom
-\sum_^\dbinom(-4)^i=(x-m)\dbinom.
Proofs
After Sun's publicatio ...
: In
combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...
, Sun's curious identity is the following
identity
Identity may refer to:
* Identity document
* Identity (philosophy)
* Identity (social science)
* Identity (mathematics)
Arts and entertainment Film and television
* ''Identity'' (1987 film), an Iranian film
* ''Identity'' (2003 film), ...
involving
binomial coefficient
In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers and is written \tbinom. It is the coefficient of the t ...
s, first established by
Zhi-Wei Sun
Sun Zhiwei (, born October 16, 1965) is a Chinese mathematician, working primarily in number theory, combinatorics, and group theory. He is a professor at Nanjing University.
Biography
Sun Zhiwei was born in Huai'an, Jiangsu. Sun and his twi ...
in 2002:
*
Tsen rank In mathematics, the Tsen rank of a field describes conditions under which a system of polynomial equations must have a solution in the field. The concept is named for C. C. Tsen, who introduced their study in 1936.
We consider a system of ''m'' p ...
: A Tsen rank of a
field
Field may refer to:
Expanses of open ground
* Field (agriculture), an area of land used for agricultural purposes
* Airfield, an aerodrome that lacks the infrastructure of an airport
* Battlefield
* Lawn, an area of mowed grass
* Meadow, a grass ...
describes conditions under which a system of
polynomial equations
In mathematics, an algebraic equation or polynomial equation is an equation of the form
:P = 0
where ''P'' is a polynomial with coefficients in some field (mathematics), field, often the field of the rational numbers. For many authors, the term '' ...
must have a solution in the field. It was introduced by mathematician
Chiungtze C. Tsen
Chiungtze C. Tsen (; Chang-Du Gan: sɛn˦˨ tɕjuŋ˨˩˧ tsɹ̩˦˨ April 2, 1898 – October 1, 1940), given name Chiung (), was a Chinese mathematician born in Nanchang, Jiangxi. He is known for his work in algebra. He was one of Emmy Noeth ...
in 1936.
*
Wu's method
Wu Wenjun, Wenjun Wu's method is an algorithm for solving systems of polynomial equations, multivariate polynomial equations introduced in the late 1970s by the Chinese mathematician Wu Wenjun, Wen-Tsun Wu. This method is based on the mathematical ...
: Wu's method was discovered in 1978 by Chinese mathematician
Wen-Tsun Wu. The method is an algorithm for solving
multivariate polynomial equations, based on the mathematical concept of characteristic set introduced in the late 1940s by
J.F. Ritt.
*
Yunnan Baiyao
Yunnan Baiyao (or Yunnan Paiyao; ) is a proprietary traditional Chinese medicine marketed and used as a hemostatic product in both human and veterinary alternative medicine. Although Yunnan Baiyao has long been recognized as a pharmaceutical prep ...
See also
*
Chinese exploration Chinese exploration includes exploratory Chinese travels abroad, on land and by sea, from the travels of Han dynasty diplomat Zhang Qian into Central Asia during the 2nd century BC until the Ming dynasty treasure voyages of the 15th century that cro ...
*
List of China-related topics
The following outline is provided as an overview of and topical guide to China:
The People's Republic of China is the most extensive country in East Asia and the third most extensive country in the world. With a population of over 1,400,000 ...
*
List of Chinese inventions
China has been the source of many innovations, scientific discoveries and inventions. This includes the ''Four Great Inventions'': papermaking, the compass, gunpowder, and printing (both woodblock and movable type). The list below contains the ...
*
List of inventions and discoveries of Neolithic China
China has been the source of many innovations, scientific discoveries and inventions. Below is an alphabetical list of inventions and discoveries made by Neolithic cultures of China and those of its prehistorical early Bronze Age before the pal ...
*
History of Chinese archaeology
Chinese archaeology has been practiced since the Song dynasty (960-1279) with early practices of antiquarianism. Although native Chinese antiquarianism developed some rigorous methods of unearthing, studying, and cataloging ancient artifacts, th ...
*
History of science and technology in China
*
History of typography in East Asia
Printing in East Asia originated from the Han dynasty (220 BCE – 206 CE) in China, evolving from ink rubbings made on paper or cloth from texts on stone tables used during the Han. Printing is considered one of the Four Great Inventions of China ...
Notes
References
Citations
Sources
* Arndt, Jörg, and Christoph Haenel. (2001). ''Pi Unleashed''. Translated by Catriona and David Lischka. Berlin: Springer. .
* Aufderheide, A. C.; Rodriguez-Martin, C. & Langsjoen, O. (1998). ''The Cambridge Encyclopedia of Human Paleopathology''. Cambridge University Press. .
* Berggren, Lennart,
Jonathan M. Borwein, and
Peter B. Borwein. (2004). ''Pi: A Source Book''. New York: Springer. .
* Chan, Alan Kam-leung and Gregory K. Clancey, Hui-Chieh Loy (2002). ''Historical Perspectives on East Asian Science, Technology and Medicine''. Singapore:
Singapore University Press
NUS Press is an academic press in Singapore. It traces its origins to the Singapore University Press, which the University of Singapore established in 1971 as its publishing arm. The press specialises in books and journals that deal with topics ...
.
*
* Elisseeff, Vadime. (2000). ''The Silk Roads: Highways of Culture and Commerce''. New York: Berghahn Books. .
* Gupta, R C. "Madhava's and other medieval Indian values of pi," in ''Math'', Education, 1975, Vol. 9 (3): B45–B48.
* Ho, Peng Yoke. "Chinese Science: The Traditional Chinese View," ''
Bulletin of the School of Oriental and African Studies
Bulletin or The Bulletin may refer to:
Periodicals (newspapers, magazines, journals)
* Bulletin (online newspaper), a Swedish online newspaper
* ''The Bulletin'' (Australian periodical), an Australian magazine (1880–2008)
** Bulletin Debate, ...
'', University of London, Vol. 54, No. 3 (1991): 506–519.
*
*
*
*
* Medvei, Victor Cornelius. (1993). ''The History of Clinical Endocrinology: A Comprehensive Account of Endocrinology from Earliest Times to the Present Day''. New York: Pantheon Publishing Group Inc. .
*
Needham, Joseph. (1986). ''Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth''. Taipei: Caves Books, Ltd.
* Needham, Joseph (1986). ''Science and Civilization in China: Volume 4, Physics and Physical Technology; Part 1, Physics''. Taipei: Caves Books Ltd.
* Salomon, Richard (1998), ''Indian Epigraphy: A Guide to the Study of Inscriptions in Sanskrit, Prakrit, and the Other Indo-Aryan Languages''. Oxford: Oxford University Press. .
*
Sivin, Nathan (1995). ''Science in Ancient China: Researches and Reflections''. Brookfield, Vermont: VARIORUM, Ashgate Publishing.
*
*
Teresi, Dick. (2002). ''Lost Discoveries: The Ancient Roots of Modern Science–from the Babylonians to the Mayas''. New York: Simon and Schuster. .
*
Wilson, Robin J. (2001). ''Stamping Through Mathematics''. New York: Springer-Verlag New York, Inc.
{{DEFAULTSORT:Chinese discoveries
Discoveries
Discoveries
China
China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and ...
Discoveries