Aside from many original inventions, the Chinese were also early original pioneers in the discovery of natural phenomena which can be found in the human body, the environment of the world, and the immediate solar system. They also discovered many concepts in mathematics. The list below contains discoveries which found their origins in China.
Imperial China 
(202 BC – 220 AD) paintings on tile of Chinese guardian spirits representing 11 pm to 1 am (left) and 5 am to 7 am (right); the ancient Chinese, although discussing it in supernatural terms, acknowledged circadian rhythm
within the human body
- Chinese remainder theorem: The Chinese remainder theorem, including simultaneous congruences in number theory, was first created in the 3rd century AD by the mathematician Sunzi, whose Mathematical Classic by Sun Zi (孙子算经, Sunzi suanjing) 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." This method of calculation was used in calendrical mathematics by Tang Dynasty (618–907) mathematicians such as Li Chunfeng (602–670) and Yi Xing (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 methods of the ancient Yijing. Its use was lost for centuries until Qin Jiushao (c. 1202–1261) revived it in his Mathematical Treatise in Nine Sections of 1247, providing constructive proof for it.
- Circadian rhythm, recognition of: The Huangdi Neijing, compiled by the 2nd century BC during the Han Dynasty (202 BC – 220 AD), noted the symptoms, behavior, and reactions of people with different diseases (i.e. of the liver, heart, spleen, lung, or kidneys) during different times of a 24-hour day. The idea of any organism following a daily circadian rhythm was not accepted in mainstream modern medical science even up until the 1960s, yet it is now well established that patients with Parkinson's disease lose much of their debilitating symptoms between 9 pm and midnight, while paroxysms of patients with asthma usually occur at night when secretion of hormones from the cortexes of the adrenal glands falls to a minimum. Although the ancient Chinese explained symptoms of diseased patients that followed the pattern of their circadian rhythms in terms of superstitious numerology and cyclic lore, they still documented such cases and expounded on them long before anyone else. 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.
- Climate change, concept of: In his Dream Pool Essays of 1088, Shen Kuo (1031–1095) wrote about a landslide (near modern Yan'an) where petrified bamboos were discovered in a preserved state underground, in the dry northern climate zone of Shanbei, Shaanxi; 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 occurred over time. Shen also advocated a hypothesis in line with geomorphology after he observed a stratum of marine fossils running in a horizontal span across a cliff of the Taihang Mountains, 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).
- Decimal fractions: As proven by inscriptions from the 13th century BC, the decimal system existed in China since the Shang Dynasty (c. 1600–c. 1050 BC). The earliest evidence of a decimal fraction, where the fraction's denominator is a power of ten, appears on an inscription of a standard measure of volume used by the mathematician and astronomer Liu Xin (c. 46 BC–23 AD), dated precisely 5 AD. The first significant piece of Chinese literature to feature decimal fractions was The Nine Chapters on the Mathematical Art. This text was first mentioned in 179 AD, although Liu Hui (fl. 3rd century AD) asserts that some of its material predates the infamous Qin book burning in 213 BC (i.e. older than the oldest surviving Chinese mathematical treatise, the Book on Numbers and Computation, 202–186 BC). Liu Hui used decimal fractions with measurements and as solutions to equations. At first decimal fractions were written in word form, since it was Han Yan (fl. late 8th century) of the Tang Dynasty (607–907) who first used modern decimal notation to write out decimal fractions. Decimal fractions were vital to the work of Song (960–1279) mathematicians such as Yang Hui (1238–1298) and Qin Jiushao (c. 1201–1261). Jamshīd al-Kāshī (1380–1429), director of the astronomical observatory at Samarkand, adopted the use of decimal fractions; they were first mentioned in Europe by Christoff Rudolff of Augsburg in his Exempel-Buechlin of 1530, yet not given serious attention until the 1585 work of the Flemish mathematician Simon Stevin (1548–1620).
The frontispiece to Hu Sihui
's Principles of Correct Diet
published in 1330 (Yuan Dynasty); the caption reads "Many diseases can be cured by diet alone," a belief which spanned back to at least the 3rd century AD in China.
- Diabetes, recognition and treatment of: The Huangdi Neijing 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 Perscriptions written by the Tang Dynasty physician Zhen Quan (died 643) was the first known book to mention an excess of sugar in the urine of diabetic patients. While his book is now lost, quotations of it were preserved in the Important Medical Formulae and Prescriptions Now Revealed by the Governor of a Distant Province, written by Wang Tao in 752. The Tang physician Sun Simiao (581–682) wrote in his Thousand Golden Remedies of 655 that for diabetic patients "three things must be renounced, wine, sex, and eating salted, starchy cereal products; if this regimen can be observed, cure may follow without drugs." Robert Temple writes that this is similar to the modern method of avoiding alcohol and starchy foods. The sweetness of urine in diabetic patients is also noted in an ancient text of India, but unlike the Chinese texts its date is ambiguous.
- Endocrinology, isolation of sex and pituitary hormones from urine: In 1110, a Chinese medical text specified the use of gypsum (containing calcium sulfate) as well as saponin from the beans of Gleditschia sinensis to extract hormones from urine, a process of using natural soaps which was not discovered elsewhere until the use of digitonin by Adolf Windaus (1876–1959) in 1909. In 1927, Selmar Ascheim (1878–1965) and Bernhard Zondek (1891–1966) discovered that urine of pregnant women had a high concentration of steroid sex hormones; a subsequent discovery was made that urine contained sex hormones of androgens and estrogens, as well as the pituitary hormone gonadotrophin. In modern medicine, the extraction of these hormones from urine is a standard practice, yet centuries before this the Chinese had used it to treat hypogonadism, impotence, spermatorrhea, dysmenorrhea, leukorrhea, and even stimulating the growth of beards (since they knew that castration resulted in the loss of ability to grow a beard).
- Equal temperament: During the Han Dynasty (202 BC–220 AD), the music theorist and mathematician Jing Fang (78–37 BC) extended the 12 tones found in the 2nd century BC Huainanzi to 60. While generating his 60-divisional tuning, he discovered that 53 just fifths is approximate to 31 octaves, calculating the difference at ; this was exactly the same value for 53 equal temperament calculated by the German mathematician Nicholas Mercator (c. 1620–1687) as 353/284, a value known as Mercator's Comma. The Ming Dynasty (1368–1644) music theorist Zhu Zaiyu (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 mathematician Simon Stevin (1548–1620) discovered the mathematical formula for equal temperament at roughly the same time (within 1 to 25 years of Zhu), yet he did not publish his work and it remained unknown until 1884; 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 1:212/12) into twelve equal semitones while each length was divided by the 12th root of 2. 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, 1:210/12, 1:29/12, etc.) and determined the exact length of the string by dividing it by 12√2 (same as 21/12). The Harmonie Universelle (1636) written by Marin Mersenne (1588–1648) was the first publication in Europe outlining equal temperament, a new system of tuning that was passionately defended by J.S. Bach (1685–1750) in his Well-Tempered Clavier of 1722.
- First law of motion, partial description: The Mohist philosophical canon of the Mojing, compiled by the followers of Mozi (c. 470 – c. 390 BC), provides the earliest known attempt to describe inertia: "The cessation of motion is due to the opposing force...If there is no opposing force...the motion will never stop. This is as true as that an ox is not a horse." However, like many of the Hundred Schools of Thought during the Warring States Period (403–221 BC), the doctrine of the Mohist sect had little impact on the course of later Chinese thought, while this passage and others from the Mojing were only given serious attention by modern scholarship after the work of Joseph Needham in 1962.
Aware of underground minerals associated with certain plants by at least the 5th century BC, the Chinese extracted trace elements of copper
from Oxalis corniculata
, pictured here, as written in the 1421 text Precious Secrets of the Realm of the King of Xin
- Geobotanical prospecting: Geobotanical prospecting can be defined as the connection made between the types of vegetation that grow in certain areas and the minerals that can be found underground in those same areas; this observation was first made in China. It is now established in modern geobotany that only certain plants can grow in soils which are rich in certain types of minerals, such as Viola calaminaria and Thlaspi which grow in soils rich in zinc. The Zhou Dynasty (c. 1050–256 BC) Chinese Classic of Mountains and Rivers, compiled from the 6th to 2nd centuries BC, states that a certain "huitang" plant only grows near ore deposits of gold. As seen in the 5th century BC text Tribute of Yu, geobotanical prospecting in ancient China was mainly concerned with describing the nature of soil in different regions for agricultural purposes. The Book of Master Wen, compiled by 380 AD and containing material from as far back as the 3rd century BC, states that the branches of trees tend to droop in soils where an abundance of jade is to be found. In about 290 AD, Zhang Hua (232–300) wrote that hematite was found in abundance in any soil where smartweed grew. In the Illustrated Mirror of the Earth, written in the early 6th century AD, there is a description of a plant with an elegant yellow stalk which was found to grow above copper, and another description of a plant with green leaves and a red stalk where lead is often found below. In his Miscellaneous Morsels from Youyang, the Tang Dynasty (618–907) author Duan Chengshi (d. 863) noted that silver could often be found in the soil where ciboule onion grew, gold where a certain kind of shallot grew, and copper where ginger grew. Su Song (1020–1101) of the Song Dynasty (960–1279) described how Portulaca oleracea could yield mercury if pounded, dried, and allowed to decay. The Precious Secrets of the Realm of the King of Xin, written in 1421 during the Ming Dynasty (1368–1644), described how mineral trace elements were observed and could be extracted from certain plants, such as copper from Oxalis corniculata, gold from rape turnip, silver from weeping willows, and lead and tin from mugwort, chestnut, barley, and wheat. Geobotanical prospecting was unknown in the rest of the world until about 1600 when Sir Thomas Challoner and his first cousin Thomas Challoner discovered alum mines on the former's property of Belman Bank, Guisborough, Yorkshire, England. Both Challoner relatives realized here (and later in Italy) that leaves of oak trees were a much darker, richer green and their branches stronger and more spread out where the alum was to be found.
- Leprosy, first description of its symptoms: The Feng zhen shi 封診式 (Models for sealing and investigating), written between 266 and 246 BC in the State of Qin during the Warring States Period (403–221 BC), is the earliest known text which describes the symptoms of leprosy, termed under the generic word li 癘 (for skin disorders). This text mentioned the destruction of the nasal septum in those suffering from leprosy (an observation that would not be made outside of China until the writings of Avicenna 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." Leprosy was not described in the West until the writings of the Roman authors Aulus Cornelius Celsus (25 BC – 37 AD) and Pliny the Elder (23–79 AD). Although it is alleged that the Indian Sushruta Samhita, which describes leprosy, is dated to the 6th century BC, India's earliest written script (besides the then long extinct Indus script)—the Brāhmī script—is thought to have been created no earlier than the 3rd century BC.
- Magic squares: The earliest magic square is the Lo Shu square, dating to 4th century BCE China. The square was viewed as mystical, and according the Chinese mythology, and "was first seen by Emperor Yu."
- Pi calculated as : The ancient Egyptians, Babylonians, Indians, and Greeks 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 π to 3.1547 as π (with evidence on vessels dating to the Wang Mang reign period, 9–23 AD, of other approximations of 3.1590, 3.1497, and 3.1679). Next, Zhang Heng (78–139 AD) made two approximations for π, by proportioning the celestial circle to the diameter of the earth as = 3.1724 and using (after a long algorithm) the square root of 10, or 3.162. In his commentary on the Han Dynasty mathematical work The Nine Chapters on the Mathematical Art, Liu Hui (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 (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 approximation for pi with a denominator of up to four digits; the next rational number is , which is the best rational approximation. 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 and Jamshīd al-Kāshī in the early 15th century.
With the description in Han Ying's written work of 135 BC (Han Dynasty
), the Chinese were the first to observe that snowflakes
had a hexagonal
- Snowflake, observation of its hexagonal structure: In his Moral Discourses Illustrating the Han Text of the Book of Songs of 135 BC, the Han Dynasty (202 BC– 220 AD) author Han Ying wrote: "Flowers of plants and trees are generally five-pointed, but those of snow, which are called ying, are always six pointed." This was the first explicit reference in world history to the hexagonal structure of snowflakes. From then on, Chinese writers throughout the centuries mentioned the hexagonal structure of snowflakes, including the crown prince and poet Xiao Tong (501–531) and the Neo-Confucian philosopher Zhu Xi (1130–1200). In contrast to Western ideas of snowflakes, Olaus Magnus (1490–1557) wrote in his A Description of the Northern Peoples in 1555 that snowflakes could take on many shapes, including crescents, arrows, nails, bells, and even the shape of the human hand. It was not until 1591 that Thomas Hariot (1560–1621) recognized the snowflake's hexagonal structure, but he did not publish his jotted private notes on the subject. Finally, the astronomer Johannes Kepler (1571–1630) wrote the first known European publication on the subject in 1611, the fifteen-page A New Year's Gift, or On the Six-Cornered Snowflake.
- Solar wind, observation of via comet tails: In the Book of Jin compiled during the Tang Dynasty (618–907), a passage written in 635 AD states: "In general, when a comet appears in the morning, its tail points towards the west, and when it appears in the evening, its tail points towards the east. This is a constant rule. If the comet is north or south of the Sun, its tail always points following the same direction as the light radiating from the Sun." In other words, as Robert Temple states, "the Chinese observations of comet tails had been refined enough to establish the principle that comet tails always point away from the sun." Furthermore, the text reveals that astronomers by at least the Tang Dynasty understood that, like the Moon, the light shining from a comet was merely reflected sunlight; from the writings of Jing Fang (78–37 BC), Wang Chong (27–100), Zhang Heng (78–139), and others it is apparent that the Chinese already by the Han Dynasty (202 BC – 220 AD) understood that the Moon was illuminated solely by the Sun's rays of light. Although the Chinese explained this constant rule about comets in terms of supernatural qi, it is now understood in modern astronomy as the concept of 'solar wind', where the powerful force of radiation from the Sun causes comets to turn away from it.
- Spontaneous combustion, recognition of: In his Record of Strange Things written sometime before 290 AD, the Jin Dynasty official and poet Zhang Hua (232–300) wrote the earliest known account acknowledging spontaneous combustion: "If ten thousand piculs of oil are accumulated in store, the oil will ignite itself spontaneously. The calamitous fire which occurred in the arsenal of the time of the Emperor Wu [of the Jin Dynasty] in the Taishi reign-period [265–74 AD] was caused by the stored oil." There were other mentionings of spontaneous combustion in early Chinese literary works, while more often than not fires were blamed on arsonists. The 13th-century work Parallel Cases Solved by Eminent Judges recounts an event in 1050 where imperial guards were charged in a court of law with the crime of allowing a fire to spread in the palace at Kaifeng; their sentence was commuted from the death penalty to a light punishment when artisans confessed that the chemical-enhanced (perhaps quicklime) oily curtains they made had the propensity to catch fire spontaneously when left out in the open, a statement which convinced Emperor Renzong (r. 1022–1063) since a random fire had recently started in oiled garments of Emperor Zhenzong's (r. 997–1022) mausoluem. The author of Parallel Cases Solved by Eminent Judges noted that Zhang Hua had once believed oil stored in an arsenal spontaneously combusted, yet he concludes that what happened in that ancient arsenal was most likely the result of oiled garments, not just oil by itself. The first acknowledgement of spontaneous combustion anywhere else in the world was made by J. P. F. Duhamel in a French scientific paper published in 1757, in which he described oiled canvas sails catching fire after being left out in the summer sun for only a few hours.
- Sunspots, recognition of as solar phenomena: The astronomer Gan De (fl. 4th century BC) from the State of Qi during the Warring States Period (403–221 BC) was the first known writer to attribute sunspots as characteristics of the sun and true solar phenomena. The next known recording of a sunspot in China was in 165 BC, yet the first precisely dated sunspot observed from China occurred on May 10, 28 BC, during the Han Dynasty (202 BC – 220 AD). From 28 BC to 1368 AD, a total of 112 other instances of sunspots were recorded by the Chinese. In the West, from the time of Aristotle (384–322 BC) of ancient Greece to the time of Galileo Galilei (1564–1642), it was commonly believed that the heavens were perfect, including the sun. After the first written observation in the West of sunpots by Einhard (d. 840) in his Life of Charlemagne in 807 AD, the sun's periodic blemishes were explained by Western thinkers as being small invisible satellites or transits of Mercury and Venus; it was only in the 17th century that these beliefs were overturned.
- True north, concept of: The Song Dynasty (960–1279) official Shen Kuo (1031–1095), alongside his colleague Wei Pu, 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, 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. When making the first known experiments with a magnetic compass, 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, and wrote that the compass needle in fact pointed towards the magnetic north pole instead of true north (indicated by the current pole star); this was a critical step in the history of accurate navigation with a compass.
- Chen's theorem: Chen's theorem states that every sufficiently large even number can be written as the sum of either two primes, or a prime and a semiprime, and was first proven by Chen Jingrun in 1966, with further details of the proof in 1973.
- Cheng's eigenvalue comparison theorem: Cheng's theorem was introduced in 1975 by Hong Kong mathematician Shiu-Yuen Cheng. It 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 because the notion of "size" of the domain must also account for its curvature.
- Chern class: Chern classes are characteristic classes in mathematics first introduced by Shiing-Shen Chern in 1946.[a]
- Culturing Chlamydia trachomatis bacteria: Chlamydia trachomatis agent was first cultured in the yolk sacs of eggs by Chinese scientists in 1957 
- Heterosis in rice, three-line hybrid rice system: A team of agricultural scientists headed by Yuan Longping applied heterosis 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 m2). 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 in agriculture for his work.
- Huang-Minglon modification: The Huang-Minglon modification, introduced by Chinese chemist Huang Minglon, is a modification of the Wolff–Kishner reduction and involves heating the carbonyl compound, potassium hydroxide, and hydrazine hydrate together in ethylene glycol in a one-pot reaction.
- Feathered theropods: The first feathered dinosaur outside of Avialae, Sinosauropteryx, meaning "Chinese reptilian wing," was discovered in the Yixian Formation 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 and John Ostrom, 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.
- Lee–Yang theorem: The Lee-Yang theorem in statistical mechanics was first proved for the Ising model by future Nobel laureates Tsung-Dao Lee and Chen Ning Yang in 1952. The theorem states that if partition functions of certain models in statistical field theory 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.[b]
- Tsen rank: A Tsen rank of a field describes conditions under which a system of polynomial equations must have a solution in the field. It was introduced by mathematician Chiungtze C. Tsen in 1936.
- Wu's method: 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.
See also 
- ^ Chern later acquired American citizenship in 1961. He was born in Jiaxing, Zhejiang.
- ^ Yang later acquired American citizenship in 1964, Lee in 1962. Both men were born in China.
- ^ a b c d Ho (1991), 516.
- ^ Temple (1986), 125.
- ^ Temple (1986), 124–125.
- ^ Temple (1986), 126.
- ^ Gwei-Djen Lu (25 October 2002). Celestial Lancets. Psychology Press. pp. 137–140. ISBN 978-0-7007-1458-2.
- ^ Chan, Clancey, Loy (2002), 15.
- ^ Needham (1986), Volume 3, 614.
- ^ Sivin (1995), III, 23.
- ^ Needham (1986), Volume 3, 603–604, 618.
- ^ Temple (1986), 139.
- ^ Temple (1986), 142–143.
- ^ a b c d e Temple (1986), 143.
- ^ a b Needham (1986), Volume 3, 24–25.
- ^ Straffin (1998), 165.
- ^ a b c d e Temple (1986), 131.
- ^ a b Temple (1986), 132.
- ^ Medvei (1993), 49.
- ^ a b c Temple (1986), 133.
- ^ Temple (1986), 128–129.
- ^ Temple (1986), 127.
- ^ Temple (1986), 130.
- ^ Temple (1986), 199.
- ^ McClain and Ming (1979), 206.
- ^ McClain and Ming (1979), 207–208.
- ^ McClain and Ming (1979), 212.
- ^ Needham (1986), Volume 4, Part 1, 218–219.
- ^ Kuttner (1975), 166–168.
- ^ Needham (1986), Volume 4, Part 1, 227–228.
- ^ a b Temple (1986), 209.
- ^ a b Needham (1986), Volume 4, Part 1, 223.
- ^ a b c d e f Temple (1986), 161.
- ^ Needham (1986), Volume 3, 24–25, 121.
- ^ Shen, Crossley, and Lun (1999), 388.
- ^ Straffin (1998), 166.
- ^ a b c d Temple (1986), 159.
- ^ a b c d e f Temple (1986), 160.
- ^ a b c Temple (1986), 142.
- ^ a b c McLeod & Yates (1981), 152–153 & footnote 147.
- ^ Aufderheide et al, (1998), 148.
- ^ Salomon (1998), 12–13.
- ^ C. J. Colbourn; Jeffrey H. Dinitz (2 November 2006). Handbook of Combinatorial Designs. CRC Press. p. 525. ISBN 978-1-58488-506-1.
- ^ a b c d Temple (1986), 141.
- ^ Teresi (2002), 65–66.
- ^ Neehdam (1986), Volume 3, 99–100.
- ^ a b Berggren, Borwein & Borwein (2004), 27
- ^ Arndt and Haenel (2001), 177
- ^ Wilson (2001), 16.
- ^ Needham (1986), Volume 3, 100–101.
- ^ Berggren, Borwein & Borwein (2004), 24–26.
- ^ Berggren, Borwein & Borwein (2004), 26.
- ^ Berggren, Borwein & Borwein (2004), 20.
- ^ Gupta (1975), B45–B48
- ^ Berggren, Borwein, & Borwein (2004), 24.
- ^ a b c d Temple (1986), 162.
- ^ a b c d Temple (1986), 34.
- ^ Needham (1986), Volume 3, 227 & 411–414.
- ^ Temple (1986), 166–167.
- ^ a b c d Temple (1986), 167.
- ^ a b c Temple (1986), 29.
- ^ Temple (1986), 30.
- ^ Temple (1986), 29–30.
- ^ Sivin (1995), III, 17–18.
- ^ Sivin (1995), III, 22.
- ^ Needham (1986), Volume 3, 278.
- ^ Sivin (1995), III, 21–22.
- ^ Elisseeff (2000), 296.
- ^ Hsu (1988), 102.
- ^ Chen, J.R. (1966). "On the representation of a large even integer as the sum of a prime and the product of at most two primes". Kexue Tongbao 17: 385–386.
- ^ Chen, J.R. (1973). "On the representation of a larger even integer as the sum of a prime and the product of at most two primes". Sci. Sinica 16: 157–176.
- ^ Cheng, Shiu Yuen (1975a). "Eigenfunctions and eigenvalues of Laplacian". Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Stanford Univ., Stanford, Calif., 1973), Part 2. Providence, R.I.: American Mathematical Society. pp. 185–193. MR 0378003.
- ^ Chavel, Isaac (1984). Eigenvalues in Riemannian geometry. Pure Appl. Math. 115. Academic Press.
- ^ Chern, S. S. (1946). "Characteristic classes of Hermitian Manifolds". Annals of Mathematics. Second Series (The Annals of Mathematics, Vol. 47, No. 1) 47 (1): 85–121. doi:10.2307/1969037. ISSN 0003-486X. JSTOR 1969037.
- ^ S Darougar, B R Jones, J R Kimptin, J D Vaughan-Jackson, and E M Dunlop. Chlamydial infection. Advances in the diagnostic isolation of Chlamydia, including TRIC agent, from the eye, genital tract, and rectum. Br J Vener Dis. 1972 December; 48(6): 416–420; TANG FF, HUANG YT, CHANG HL, WONG KC. Further studies on the isolation of the trachoma virus. Acta Virol. 1958 Jul-Sep;2(3):164-70; TANG FF, CHANG HL, HUANG YT, WANG KC. Studies on the etiology of trachoma with special reference to isolation of the virus in chick embryo. Chin Med J. 1957 Jun;75(6):429-47; TANG FF, HUANG YT, CHANG HL, WONG KC. Isolation of trachoma virus in chick embryo. J Hyg Epidemiol Microbiol Immunol. 1957;1(2):109-20
- ^ Sant S. Virmani, C. X. Mao, B. Hardy, (2003). Hybrid Rice for Food Security, Poverty Alleviation, and Environmental Protection. International Rice Research Institute. ISBN 971-22-0188-0, p. 248
- ^ Wolf Foundation Agricultural Prizes
- ^ Huang-Minlon Journal of the American Chemical Society 1946, 68, 2487.
- ^ Huang-Minlon Journal of the American Chemical Society 1949, 71, 3301.
- ^ Organic Syntheses, Coll. Vol. 4, p. 510 (1963); Vol. 38, p. 34 (1958). (Article)
- ^ Ji Qiang; & Ji Shu-an (1996). "On the discovery of the earliest bird fossil in China and the origin of birds" (PDF). Chinese Geology 233: 30–33.
- ^ Browne, M.W. (19 October 1996). "Feathery Fossil Hints Dinosaur-Bird Link". New York Times. p. Section 1 page 1 of the New York edition.
- ^ Chen Pei-ji, Pei-ji; Dong Zhiming; & Zhen Shuo-nan. (1998). "An exceptionally preserved theropod dinosaur from the Yixian Formation of China". Nature 391 (6663): 147–152. Bibcode:1998Natur.391..147C. doi:10.1038/34356.
- ^ Sanderson, K. (23 May 2007). "Bald dino casts doubt on feather theory". doi:10.1038/news070521-6. Retrieved 14 January 2011.
- ^ Yang, C. N.; Lee, T. D. (1952). "Statistical Theory of Equations of State and Phase Transitions. I. Theory of Condensation". Physical Review 87: 404–409. doi:10.1103/PhysRev.87.404. ISSN 0031-9007.
- ^ Tsen, C. (1936). "Zur Stufentheorie der Quasi-algebraisch-Abgeschlossenheit kommutativer Körper". J. Chinese Math. Soc. 171: 81–92. Zbl 0015.38803.
- ^ Wu, Wen-Tsun (1978). "On the decision problem and the mechanization of theorem proving in elementary geometry". Scientia Sinica 21.
- ^ P. Aubry, D. Lazard, M. Moreno Maza (1999). On the theories of triangular sets. Journal of Symbolic Computation, 28(1–2):105–124
- Arndt, Jörg, and Christoph Haenel. (2001). Pi Unleashed. Translated by Catriona and David Lischka. Berlin: Springer. ISBN 3-540-66572-2.
- Aufderheide, A. C.; Rodriguez-Martin, C. & Langsjoen, O. (1998). The Cambridge Encyclopedia of Human Paleopathology. Cambridge University Press. ISBN 0-521-55203-6.
- Berggren, Lennart, Jonathan M. Borwein, and Peter B. Borwein. (2004). Pi: A Source Book. New York: Springer. ISBN 0-387-20571-3.
- 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. ISBN 9971-69-259-7
- Elisseeff, Vadime. (2000). The Silk Roads: Highways of Culture and Commerce. New York: Berghahn Books. ISBN 1-57181-222-9.
- 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, University of London, Vol. 54, No. 3 (1991): 506-519.
- Hsu, Mei-ling. "Chinese Marine Cartography: Sea Charts of Pre-Modern China," in Imago Mundi, Volume 40 (1988): 96–112.
- McLeod, Katrina C. D. and Robin D. S. Yates. "Forms of Ch'in Law: An Annotated Translation of The Feng-chen shih," Harvard Journal of Asiatic Studies, Vol. 41, No. 1 (Jun., 1981): 111-163.
- McClain, Ernest G. and Ming Shui Hung. "Chinese Cyclic Tunings in Late Antiquity," Ethnomusicology, Vol. 23, No. 2 (May, 1979): 205-224.
- 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. ISBN 1-85070-427-9.
- 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. ISBN 0-19-509984-2.
- Sivin, Nathan (1995). Science in Ancient China: Researches and Reflections. Brookfield, Vermont: VARIORUM, Ashgate Publishing.
- Straffin, Philip D., Jr. "Liu Hui and the First Golden Age of Chinese Mathematics," Mathematics Magazine, Vol. 71, No. 3 (Jun., 1998): 163-181.
- Temple, Robert. (1986). The Genius of China: 3,000 Years of Science, Discovery, and Invention. With a forward by Joseph Needham. New York: Simon and Schuster, Inc. ISBN 0-671-62028-2.
- Teresi, Dick. (2002). Lost Discoveries: The Ancient Roots of Modern Science–from the Babylonians to the Mayas. New York: Simon and Schuster. ISBN 0-684-83718-8.
- Wilson, Robin J. (2001). Stamping Through Mathematics. New York: Springer-Verlag New York, Inc.