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| {{History of science and technology in China}}
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| [[List of Chinese inventions|Aside from many original inventions]], the [[Zhonghua minzu|Chinese]] were also early original pioneers in the discovery of natural phenomena which can be found in the [[human body]], the environment of the [[Earth|world]], and the immediate [[solar system]]. They also discovered many concepts in [[Chinese mathematics|mathematics]]. The list below contains discoveries which found their origins in [[China]].
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| ==Discoveries==
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| ===Imperial China===
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| [[File:Guardians of Day and Night, Han Dynasty.jpg|thumb|right|[[Han Dynasty]] (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]]
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| * '''[[Chinese remainder theorem]]''': The Chinese remainder theorem, including [[Modular arithmetic|simultaneous congruences]] in [[number theory]], was first created in the 3rd century AD by the mathematician [[Sun Tzu (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."<ref name="ho 1991 516">Ho (1991), 516.</ref> 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 ([[Naked-eye planet|those discerned by the naked eye]]).<ref name="ho 1991 516"/> Thus, it was strongly associated with the [[divination]] methods of the ancient ''[[Yijing]]''.<ref name="ho 1991 516"/> 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.<ref name="ho 1991 516"/>
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| * '''[[Decimal#Decimal fractions|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).<ref name="temple 1986 139">Temple (1986), 139.</ref> The earliest evidence of a decimal [[Fraction (mathematics)|fraction]], where the fraction's [[denominator]] is a [[exponentiation|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.<ref name="temple 1986 142 143">Temple (1986), 142–143.</ref> The first significant piece of Chinese literature to feature decimal fractions was ''[[The Nine Chapters on the Mathematical Art]]''.<ref name="temple 1986 143">Temple (1986), 143.</ref> This text was first mentioned in 179 AD,<ref name="needham volume 3 24 25">Needham (1986), Volume 3, 24–25.</ref> although [[Liu Hui]] (fl. 3rd century AD) asserts that some of its material predates the [[Burning of books and burying of scholars|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).<ref>Straffin (1998), 165.</ref> Liu Hui used decimal fractions with measurements and as solutions to [[equation]]s.<ref name="temple 1986 143" /> 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.<ref name="temple 1986 143" /> Decimal fractions were vital to the work of [[Song Dynasty|Song]] (960–1279) mathematicians such as [[Yang Hui]] (1238–1298) and [[Qin Jiushao]] (c. 1201–1261).<ref name="temple 1986 143" /> [[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 people|Flemish]] mathematician [[Simon Stevin]] (1548–1620).<ref name="temple 1986 143" />
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| [[File:Principles of Correct Diet, Yuan Dynasty, 1330.jpg|thumb|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.<ref name="temple 1986 131"/>]]
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| * '''[[Nutrition disorder|Deficiency diseases, correction by proper diet]]''': As early as the 4th century BC, [[Warring States period]] (403–221 BC), records indicate that [[Dietician|Imperial Dieticians]] were appointed at royal courts.<ref name="temple 1986 131">Temple (1986), 131.</ref> The first explicit description of a regulated diet used to curb certain diseases is found in the ''[[Jinkui Yaolue|Systematic Treasury of Medicine]]'' written by [[Zhang Zhongjing]] (c. 150 – c. 219) during the late Han Dynasty.<ref name="temple 1986 131"/> Although Zhang did not understand the true nature of [[vitamin]]s, he prescribed foods now known to be rich in certain vitamins, which were discovered to be useful after much trial and error.<ref name="temple 1986 131"/> The Yuan Dynasty (1271–1368) physician and Imperial Dietician [[Hu Sihui]] (fl. 1314–1330) published his book ''Principles of Correct Diet'' which compiled a large amount of previous material written on the subject.<ref name="temple 1986 131"/>
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| * '''[[Diabetes|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.<ref name="temple 1986 132">Temple (1986), 132.</ref><ref name="medvei 1993 49">Medvei (1993), 49.</ref> 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.<ref name="temple 1986 132"/> 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."<ref name="temple 1986 133">Temple (1986), 133.</ref> Robert Temple writes that this is similar to the modern method of avoiding alcohol and [[starch]]y foods.<ref name="temple 1986 133"/> 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.<ref name="temple 1986 133"/>
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| * '''[[Endocrinology|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 Otto Reinhold Windaus|Adolf Windaus]] (1876–1959) in 1909.<ref name="temple 1986 128 129">Temple (1986), 128–129.</ref> In 1927, [[Selmar Ascheim]] (1878–1965) and [[Bernhard Zondek]] (1891–1966) discovered that urine of [[pregnancy|pregnant women]] had a high concentration of [[Sex steroid|steroid sex hormones]]; a subsequent discovery was made that urine contained sex hormones of [[androgen]]s and [[estrogen]]s, as well as the [[Pituitary gland|pituitary]] hormone [[gonadotrophin]].<ref name="temple 1986 127">Temple (1986), 127.</ref> 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]], [[Erectile dysfunction|impotence]], [[spermatorrhea]], [[dysmenorrhea]], [[leukorrhea]], and even stimulating the growth of [[beard]]s (since they knew that [[castration]] resulted in the loss of ability to grow a beard).<ref>Temple (1986), 130.</ref>
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| [[File:Bianzhong.jpg|thumb|Each [[bianzhong of Marquis Yi of Zeng|bronze bell of Marquis Yi of Zeng]] (433 BC) bears an inscription describing the specific note it plays, its position on a [[Musical scale|12-note scale]], and how this scale differed from scales [[Warring States period|used by other Chinese states]] of the time; before this discovery in 1978,<ref name="temple 1986 199">Temple (1986), 199.</ref> the oldest known surviving Chinese tuning set came from [[Guanzi (text)|a 3rd-century BC text]] (which alleges was written by [[Guan Zhong]], d. 645 BC) with five tones and additions or subtractions of ⅓ of successive tone values which produce the [[Circle of fifths|rising fourths and falling fifths]] of [[Pythagorean comma|Pythagorean tuning]].<ref>McClain and Ming (1979), 206.</ref>]]
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| * '''[[Equal temperament]]''': During the [[Han Dynasty]] (202 BC–220 AD), the [[Music theory|music theorist]] and mathematician [[Jing Fang]] (78–37 BC) extended [[Chromatic scale|the 12 tones]] found in the 2nd century BC ''[[Huainanzi]]'' to 60.<ref>McClain and Ming (1979), 207–208.</ref> While generating his 60-divisional tuning, he discovered that 53 [[just fifth]]s is approximate to 31 [[octave]]s, calculating the difference at <math>\tfrac{177147}{176776}</math>; this was exactly the same value for [[53 equal temperament]] calculated by the [[Germans|German]] mathematician [[Nicholas Mercator]] (c. 1620–1687) as 3<sup>53</sup>/2<sup>84</sup>, a value known as [http://www.tonalsoft.com/enc/m/mercator-comma.aspx Mercator's Comma].<ref>McClain and Ming (1979), 212.</ref><ref>Needham (1986), Volume 4, Part 1, 218–219.</ref> 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 people|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.<ref>Kuttner (1975), 166–168.</ref><ref>Needham (1986), Volume 4, Part 1, 227–228.</ref><ref name="temple 1986 209"/> In order to obtain [[Interval (music)|equal intervals]], Zhu divided the octave (each octave with a ratio of 1:2, which can also be expressed as 1:2<sup>12/12</sup>) into twelve equal [[semitone]]s while each length was divided by the 12th root of 2.<ref name="needham volume 4 part 1 223">Needham (1986), Volume 4, Part 1, 223.</ref> 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 <sup>11/12</sup>, 1:2<sup>10/12</sup>, 1:2<sup>9/12</sup>, etc.) and determined the exact length of the string by dividing it by <sup>12</sup>√<span style = "text-decoration:overline">2</span> (same as 2<sup>1/12</sup>).<ref name="needham volume 4 part 1 223"/> 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 [[Johann Sebastian Bach|J.S. Bach]] (1685–1750) in his ''[[Well-Tempered Clavier]]'' of 1722.<ref name="temple 1986 209">Temple (1986), 209.</ref>
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| * '''[[Newton's laws of motion|First law of motion, partial description]]''': The [[Mohism|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."<ref name="temple 1986 161">Temple (1986), 161.</ref> 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.<ref name="temple 1986 161"/>
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| * '''[[Gaussian elimination]]''': First published [[Western world|in the West]] by [[Carl Friedrich Gauss]] (1777–1855) in 1826, the algorithm for [[System of linear equations|solving linear equations]] known as Gaussian elimination is named after this [[Kingdom of Hanover|Hanoverian]] mathematician, yet it was first expressed as the Array Rule in the Chinese ''[[Nine Chapters on the Mathematical Art]]'', written at most by 179 AD during the [[Han Dynasty]] (202 BC–220 AD) and commented on by the 3rd century mathematician [[Liu Hui]].<ref>Needham (1986), Volume 3, 24–25, 121.</ref><ref>Shen, Crossley, and Lun (1999), 388.</ref><ref>Straffin (1998), 166.</ref>
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| [[File:Oxalis corniculata 1.JPG|thumb|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''.]]
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| * '''[[Geobotanical prospecting]]''': Geobotanical prospecting can be defined as the connection made between the types of vegetation that grow in certain areas and the [[mineral]]s that can be found underground in those same areas; this observation was first made in China.<ref name="temple 1986 159">Temple (1986), 159.</ref> It is now established in modern [[phytogeography|geobotany]] that only certain plants can grow in soils which are rich in certain types of minerals, such as ''[[Viola tricolor|Viola calaminaria]]'' and ''[[Thlaspi]]'' which grow in soils rich in [[zinc]].<ref name="temple 1986 159"/> 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]].<ref name="temple 1986 159"/> As seen in the 5th century BC text ''[[Yu the Great|Tribute of Yu]]'', geobotanical prospecting in ancient China was mainly concerned with describing the nature of soil in different regions for agricultural purposes.<ref name="temple 1986 159"/> The ''[[Wenzi|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.<ref name="temple 1986 160">Temple (1986), 160.</ref> In about 290 AD, [[Zhang Hua]] (232–300) wrote that [[hematite]] was found in abundance in any soil where [[Polygonum|smartweed]] grew.<ref name="temple 1986 160"/> 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.<ref name="temple 1986 160"/> 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 [[Welsh onion|ciboule onion]] grew, gold where a certain kind of [[shallot]] grew, and copper where [[ginger]] grew.<ref name="temple 1986 160"/> [[Su Song]] (1020–1101) of the [[Song Dynasty]] (960–1279) described how ''[[Portulaca oleracea]]'' could yield [[Mercury (element)|mercury]] if pounded, dried, and allowed to decay.<ref name="temple 1986 160"/> 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 [[Salix babylonica#Horticultural selections and related hybrids|weeping willows]], and lead and [[tin]] from [[mugwort]], [[chestnut]], [[barley]], and [[wheat]].<ref name="temple 1986 160"/> 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]].<ref name="temple 1986 161"/> 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.<ref name="temple 1986 161"/>
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| * '''[[Horner scheme]]''': Although named after [[English people|English]] mathematician [[William George Horner]] (1786–1837), the Horner scheme, an [[algorithm]] used to estimate the root of an equation and evaluate [[polynomial]]s in [[Monomial basis|monomial form]], was actually first invented in China to find the [[cube root]] of the number 1,860,867 (the answer given being 123).<ref name="temple 1986 142">Temple (1986), 142.</ref> This is found in the [[Han Dynasty]] (202 BC–220 AD) work ''[[The Nine Chapters on the Mathematical Art]]'', commented on by [[Liu Hui]] (fl. 3rd century) in 263 AD.<ref name="temple 1986 142"/> The original ''Nine Chapters'' found the root of equations through continued fractions, just like the later [[Italian people|Italian]] mathematician [[Joseph Louis Lagrange]] (1736–1813), while Liu Hui achieved this by increasing [[decimal]]s, just like William George Horner in his work of 1819.<ref name="temple 1986 142"/>
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| [[File:Gandhi leper.jpg|thumb|[[Mohandas Karamchand Gandhi]] tends to a leper; the Chinese were the first to describe the symptoms of [[leprosy]].]]
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| * '''[[Leprosy#History|Leprosy, first description of its symptoms]]''': The [[Shuihudi Qin bamboo texts|''Feng zhen shi'' 封診式]] (''Models for sealing and investigating''), written between 266 and 246 BC in the [[Qin (state)|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).<ref name="mcleod yates 152 153">McLeod & Yates (1981), 152–153 & footnote 147.</ref> 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]]."<ref name="mcleod yates 152 153"/> Leprosy was not described [[Western world|in the West]] until the writings of the [[Ancient Rome|Roman]] authors [[Aulus Cornelius Celsus]] (25 BC – 37 AD) and [[Pliny the Elder]] (23–79 AD).<ref name="mcleod yates 152 153"/> Although it is alleged that the Indian ''[[Sushruta Samhita]]'', which describes leprosy,<ref>Aufderheide et al, (1998), 148.</ref> 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.<ref>Salomon (1998), 12–13.</ref>
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| [[File:Yuan dynasty iron magic square.jpg|thumb|right|220px|Iron plate with an order 6 magic square in [[Arabic numbers]] from China, dating to the [[Yuan Dynasty]] (1271-1368).]]
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| *'''[[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 [[Yu the Great|Emperor Yu]]."<ref name="Colbourn">{{cite book|author1=C. J. Colbourn|author2=Jeffrey H. Dinitz|title=Handbook of Combinatorial Designs|date=2 November 2006|publisher=CRC Press|isbn=978-1-58488-506-1|pages=525}}</ref>
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| * '''[[Negative number|Negative numbers, symbols for and use of]]''': In the ''[[Nine Chapters on the Mathematical Art]]'' compiled during the [[Han Dynasty]] (202 BC–220 AD) by 179 AD and commented on by [[Liu Hui]] (fl. 3rd century) in 263,<ref name="needham volume 3 24 25"/> negative numbers appear as black rods and positive numbers as red rods in the Chinese [[counting rods]] system.<ref name="temple 1986 141">Temple (1986), 141.</ref> Liu Hui also used slanted counting rods to denote negative numbers.<ref name="temple 1986 141"/> Negative numbers denoted by a "+" sign also appear in the ancient [[Bakhshali manuscript]] of [[India]], yet scholars disagree as to when it was compiled, giving a collective range of 200 to 600 AD.<ref name="teresi 2002 65 66">Teresi (2002), 65–66.</ref> Negative numbers were known in India certainly by about 630 AD, when the mathematician [[Brahmagupta]] (598–668) used them.<ref name="temple 1986 141"/> Negative numbers were first used in Europe by the [[Roman Greece|Greek]] mathematician [[Diophantus]] (fl. 3rd century) in about 275 AD, yet were considered absurd [[Western world|in the West]] until [[Ars Magna (Gerolamo Cardano)|''The Great Art'']] written in 1545 by the [[Italy|Italian]] mathematician [[Girolamo Cardano]] (1501–1576).<ref name="temple 1986 141"/>
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| * '''[[Numerical approximations of π|Pi calculated as <math>\tfrac{355}{113}</math>]]''': The ancient [[Egyptian mathematics|Egyptians]], [[Babylonian mathematics|Babylonians]], [[Indian mathematics|Indians]], and [[Greek mathematics|Greeks]] had [[Chronology of computation of π|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).<ref>Neehdam (1986), Volume 3, 99–100.</ref><ref name="berggren borwein borwein 2004 27"/> Next, [[Zhang Heng]] (78–139 AD) made two approximations for π, by proportioning the celestial circle to the diameter of the earth as <math>\tfrac{736}{232}</math> = 3.1724 and using (after a long algorithm) the [[square root]] of 10, or 3.162.<ref name="berggren borwein borwein 2004 27">Berggren, Borwein & Borwein (2004), 27</ref><ref>Arndt and Haenel (2001), 177</ref><ref>Wilson (2001), 16.</ref> In his commentary on the [[Han Dynasty]] mathematical work ''[[The Nine Chapters on the Mathematical Art]]'', [[Liu Hui]] (fl. 3rd century) [[Liu Hui's π algorithm|used various algorithms]] to render multiple approximations for pi at 3.142704, 3.1428, and 3.14159.<ref>Needham (1986), Volume 3, 100–101.</ref> Finally, the mathematician and astronomer [[Zu Chongzhi]] (429–500) approximated pi to an even greater degree of accuracy, rendering it <math>\tfrac{355}{113}</math>, a value known in Chinese as [[Milü|Milü ("detailed ratio")]].<ref>Berggren, Borwein & Borwein (2004), 24–26.</ref> This was the best [[Rational number|rational]] approximation for pi with a [[denominator]] of up to four digits; the next rational number is <math>\tfrac{52163}{16604}</math>, which is the [[Continued fraction#Best rational approximations|best rational approximation]]. Zu ultimately determined the value for π to be between 3.1415926 and 3.1415927.<ref>Berggren, Borwein & Borwein (2004), 26.</ref> Zu's approximation was the most accurate in the world, and would not be achieved elsewhere for another millennium,<ref>Berggren, Borwein & Borwein (2004), 20.</ref> until [[Madhava of Sangamagrama]]<ref>Gupta (1975), B45–B48</ref> and [[Jamshīd al-Kāshī]]<ref>Berggren, Borwein, & Borwein (2004), 24.</ref> in the early 15th century.
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| [[File:B05n.jpg|thumb|With the description in Han Ying's written work of 135 BC ([[Han Dynasty]]), the Chinese were the first to observe that [[snowflake]]s had a [[hexagon]]al structure.]]
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| [[File:Zhenzong.jpg|thumb|Oiled garments left in the tomb of [[Emperor Zhenzong of Song]] (r. 997–1022), pictured here in this portrait, caught fire seemingly at random, a case which a 13th-century author related back to the [[spontaneous combustion]] described by [[Zhang Hua]] (232–300) around 290 AD]]
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| * '''[[Snow|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."<ref name="temple 1986 162">Temple (1986), 162.</ref> This was the first explicit reference in world history to the [[hexagon]]al structure of snowflakes.<ref name="temple 1986 162"/> 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-Confucianism|Neo-Confucian]] philosopher [[Zhu Xi]] (1130–1200).<ref name="temple 1986 162"/> In contrast to [[Western world|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.<ref name="temple 1986 161"/> 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.<ref name="temple 1986 161"/> 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''.<ref name="temple 1986 162"/>
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| * '''[[Solar wind|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."<ref name="temple 1986 34">Temple (1986), 34.</ref> 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."<ref name="temple 1986 34"/> 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;<ref name="temple 1986 34"/> 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 [[Sunlight|Sun's rays of light]].<ref>Needham (1986), Volume 3, 227 & 411–414.</ref> 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.<ref name="temple 1986 34"/>
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| * '''[[Spontaneous combustion|Spontaneous combustion, recognition of]]''': In his ''Record of Strange Things'' written sometime before 290 AD, the [[Jin Dynasty (265-420)|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."<ref name="temple 1986 166 167">Temple (1986), 166–167.</ref> There were other mentionings of spontaneous combustion in early Chinese literary works, while more often than not fires were blamed on [[arson]]ists.<ref name="temple 1986 167">Temple (1986), 167.</ref> 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 [[Calcium oxide|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.<ref name="temple 1986 167"/> 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.<ref name="temple 1986 167"/> The first acknowledgement of spontaneous combustion anywhere else in the world was made by J. P. F. Duhamel in a [[French language|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.<ref name="temple 1986 167"/>
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| * '''[[Sunspot|Sunspots, recognition of as solar phenomena]]''': The astronomer [[Gan De]] (fl. 4th century BC) from the [[Qi (state)|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.<ref name="temple 1986 29">Temple (1986), 29.</ref> 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).<ref name="temple 1986 29"/> From 28 BC to 1368 AD, a total of 112 other instances of sunspots were recorded by the Chinese.<ref name="temple 1986 30">Temple (1986), 30.</ref> [[Western world|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.<ref name="temple 1986 29"/> After the first written observation in the West of sunpots by [[Einhard]] (d. 840) in his ''[[Charlemagne|Life of Charlemagne]]'' in 807 AD, the sun's periodic blemishes were explained by Western thinkers as being small invisible satellites or [[Astrological transit|transits]] of [[Mercury (planet)|Mercury]] and [[Venus]]; it was only in the 17th century that these beliefs were overturned.<ref name="temple 1986 29 30">Temple (1986), 29–30.</ref>
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| * '''[[True north|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.<ref>Sivin (1995), III, 17–18.</ref> By doing so, Shen fixed the outdated position of the [[pole star]], which had shifted over the centuries since the time [[Zu Geng (mathematician)|Zu Geng]] (fl. 5th century) had plotted it; this was due to the [[Precession (astronomy)|precession of the Earth's]] rotational axis.<ref name="sivin III 22">Sivin (1995), III, 22.</ref><ref name="needham volume 3 278">Needham (1986), Volume 3, 278.</ref> 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.<ref name="sivin III 21 22">Sivin (1995), III, 21–22.</ref><ref>Elisseeff (2000), 296.</ref><ref>Hsu (1988), 102.</ref>
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| ===Modern===
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| *'''[[Chen's theorem]]''': Chen's theorem states that every sufficiently large even number can be written as the sum of either two [[prime number|primes]], or a prime and a [[semiprime]], and was first proven by [[Chen Jingrun]] in 1966,<ref>{{cite journal | last=Chen | first=J.R. | title=On the representation of a large even integer as the sum of a prime and the product of at most two primes | journal=Kexue Tongbao | volume=17 | year=1966 | pages=385–386}}</ref> with further details of the [[mathematical proof|proof]] in 1973.<ref name="Chen 1973">{{cite journal | last=Chen | first=J.R. | title=On the representation of a larger even integer as the sum of a prime and the product of at most two primes | journal=Sci. Sinica | volume=16 | year=1973 | pages=157–176}}</ref>
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| *'''[[Cheng's eigenvalue comparison theorem]]''': Cheng's theorem was introduced in 1975 by Hong Kong mathematician [[Shiu-Yuen Cheng]].<ref>{{cite journal | authorlink=Shiu-Yuen Cheng | last1=Cheng | first1=Shiu Yuen | title=Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Stanford Univ., Stanford, Calif., 1973), Part 2 | publisher=[[American Mathematical Society]] | location=Providence, R.I. | mr=0378003 | year=1975a | chapter=Eigenfunctions and eigenvalues of Laplacian | pages=185–193}}</ref> 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]].<ref>{{cite journal|first=Isaac|last=Chavel|title=Eigenvalues in Riemannian geometry|series=Pure Appl. Math.|volume=115|publisher=[[Academic Press]]|year=1984}}</ref>
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| *'''[[Chern class]]''': Chern classes are [[characteristic classes]] in mathematics first introduced by [[Shiing-Shen Chern]] in 1946.<ref>{{cite journal | last1=Chern | first1=S. S. | title=Characteristic classes of Hermitian Manifolds | year=1946 | journal=[[Annals of Mathematics|Annals of Mathematics. Second Series]] | issn=0003-486X | volume=47 | issue=1 | pages=85–121 | doi=10.2307/1969037 | publisher=The Annals of Mathematics, Vol. 47, No. 1 |jstor=1969037}}</ref>{{efn|Chern later acquired American citizenship in 1961. He was born in [[Jiaxing]], [[Zhejiang]].}}
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| * '''Culturing [[Chlamydia trachomatis]] bacteria''': Chlamydia trachomatis agent was first cultured in the yolk sacs of eggs by Chinese scientists in 1957 <ref>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</ref>
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| * '''[[Hybrid rice|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.<ref>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</ref> The innovation allowed for roughly 12,000 kg (26,450 lbs) of rice to be grown per hectare (10,000 m<sup>2</sup>). 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.<ref>[http://www.wolffund.org.il/cat.asp?id=14&cat_title=AGRICULTURE Wolf Foundation Agricultural Prizes]</ref>
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| *'''[[Wolff-Kishner reduction#Huang-Minglon modification|Huang-Minglon modification]]''': The Huang-Minglon modification, introduced by Chinese chemist [[Huang Minglon]],<ref>Huang-Minlon ''[[Journal of the American Chemical Society]]'' '''1946''', ''68'', 2487.</ref><ref>Huang-Minlon ''[[Journal of the American Chemical Society]]'' '''1949''', ''71'', 3301.</ref> 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 synthesis|one-pot reaction]].<ref>[[Organic Syntheses]], Coll. Vol. 4, p. 510 (1963); Vol. 38, p. 34 (1958). ([http://www.orgsyn.org/orgsyn/prep.asp?prep=cv4p0510 Article])</ref>
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| *'''[[Origin of birds#Modern research and feathered dinosaurs in China|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.<ref name=jiji1996>{{cite journal |last=Ji Qiang |coauthors=& Ji Shu-an |year=1996 |title=On the discovery of the earliest bird fossil in China and the origin of birds |journal=Chinese Geology |volume=233 |pages=30–33 | url=http://www.paleoglot.org/files/Ji&Ji_96.pdf | format = PDF}}</ref> The discovery is seen as evidence that dinosaurs [[origin of birds|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."<ref name=nyt2006>{{cite news|last=Browne|first=M.W.|title=Feathery Fossil Hints Dinosaur-Bird Link|newspaper=New York Times|date=19 October 1996 |page=Section 1 page 1 of the New York edition}}</ref> The dinosaur was covered in what are dubbed 'protofeathers' and considered to be [[Homology (biology)|homologous]] with the more advanced feathers of birds,<ref name=chenetal1998>{{cite journal |last=Chen Pei-ji |coauthors=[[Dong Zhiming]]; & Zhen Shuo-nan. |year=1998 |title=An exceptionally preserved theropod dinosaur from the Yixian Formation of China |journal=Nature |volume=391 |issue=6663 |pages=147–152 |doi=10.1038/34356 |first1=Pei-ji|bibcode = 1998Natur.391..147C }}</ref> although some scientists disagree with this assessment.<ref name=balddino>{{cite web|last=Sanderson |first=K. |url= http://www.nature.com/news/2007/070521/full/070521-6.html |title=Bald dino casts doubt on feather theory |date=23 May 2007 |doi=10.1038/news070521-6 |accessdate=14 January 2011}}</ref>
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| *'''[[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 function (statistical mechanics)|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.<ref>{{cite journal | last1=Yang | first1=C. N. | last2=Lee | first2=T. D. | title=Statistical Theory of Equations of State and Phase Transitions. I. Theory of Condensation | url=http://link.aps.org/abstract/PR/v87/p404 | doi=10.1103/PhysRev.87.404 | year=1952 | journal=[[Physical Review]] | issn=0031-9007 | volume=87 | pages=404–409|bibcode = 1952PhRv...87..404Y }}</ref>{{efn|Yang later acquired American citizenship in 1964, Lee in 1962. Both men were born in China.}}
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| *'''[[Tsen rank]]''': A Tsen rank of a [[field (mathematics)|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.<ref>{{cite journal | first=C. | last=Tsen | authorlink=C. C. Tsen | title=Zur Stufentheorie der Quasi-algebraisch-Abgeschlossenheit kommutativer Körper | journal=J. Chinese Math. Soc. | volume=171 | year=1936 | pages=81–92 | zbl=0015.38803 }}</ref>
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| *'''[[Wu's method of characteristic set|Wu's method]]''': Wu's method was discovered in 1978 by Chinese mathematician [[Wu Wenjun|Wen-Tsun Wu]].<ref>{{cite journal | last=Wu | first=Wen-Tsun | title=On the decision problem and the mechanization of theorem proving in elementary geometry | journal=Scientia Sinica | volume=21 | year=1978}}</ref> The method is an algorithm for solving [[systems of polynomial equations|multivariate polynomial equations]], based on the mathematical concept of characteristic set introduced in the late 1940s by [[Joseph Ritt|J.F. Ritt]].<ref>P. Aubry, D. Lazard, M. Moreno Maza (1999). On the theories of triangular sets. Journal of Symbolic Computation, 28(1–2):105–124</ref>
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| ==See also==
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| * [[Chinese exploration]]
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| * [[List of Chinese inventions]]
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| * [[Science and technology in China]]
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| * [[List of Japanese inventions]]
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| * [[List of Indian inventions]]
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| * [[List of Korean inventions]]
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| * [[List of Australian inventions]]
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| * [[Timeline of United States inventions]]
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| * [[Timeline of United States discoveries]]
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| * [[English inventions and discoveries]]
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| * [[Scottish inventions and discoveries]]
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| * [[Welsh inventions and discoveries]]
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| * [[Irish inventions and discoveries]]
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| * [[German inventions and discoveries]]
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| * [[Dutch inventions and discoveries]]
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| * [[Swedish inventions]]
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| * [[Science and technology of the Han Dynasty]]
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| * [[Canadian inventions]]
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| * [[Ancient Egyptian technology]]
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| * [[Ancient Greek technology]]
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| * [[Roman technology]]
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| * [[Inventions in medieval Islam]]
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| * [[Technology of the Song Dynasty]]
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| * [[History of science in Classical Antiquity]]
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| * [[History of science and technology in China]]
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| * [[History of typography in East Asia]]
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| * [[Science in Medieval Western Europe]]
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| * [[Science and technology in the United States]]
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| * [[Technological and industrial history of the United States]]
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| * [[List of China-related topics]]
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| ==Notes==
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| {{Reflist|group=lower-alpha}}
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| {{reflist|2}}
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| ==References==
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| *Arndt, Jörg, and Christoph Haenel. (2001). ''Pi Unleashed''. Translated by Catriona and David Lischka. Berlin: Springer. ISBN 3-540-66572-2.
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| * Aufderheide, A. C.; Rodriguez-Martin, C. & Langsjoen, O. (1998). ''The Cambridge Encyclopedia of Human Paleopathology''. Cambridge University Press. ISBN 0-521-55203-6.
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| *Berggren, Lennart, Jonathan M. Borwein, and Peter B. Borwein. (2004). ''Pi: A Source Book''. New York: Springer. ISBN 0-387-20571-3.
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| *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
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| *Elisseeff, Vadime. (2000). ''The Silk Roads: Highways of Culture and Commerce''. New York: Berghahn Books. ISBN 1-57181-222-9.
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| *Gupta, R C. "Madhava's and other medieval Indian values of pi," in ''Math'', Education, 1975, Vol. 9 (3): B45–B48.
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| *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.
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| *Hsu, Mei-ling. "Chinese Marine Cartography: Sea Charts of Pre-Modern China," in ''Imago Mundi'', Volume 40 (1988): 96–112.
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| *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.
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| *McClain, Ernest G. and Ming Shui Hung. "Chinese Cyclic Tunings in Late Antiquity," ''Ethnomusicology'', Vol. 23, No. 2 (May, 1979): 205-224.
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| * 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.
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| *Needham, Joseph. (1986). ''Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth''. Taipei: Caves Books, Ltd.
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| *Needham, Joseph (1986). ''Science and Civilization in China: Volume 4, Physics and Physical Technology; Part 1, Physics''. Taipei: Caves Books Ltd.
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| *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.
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| *Sivin, Nathan (1995). ''Science in Ancient China: Researches and Reflections''. Brookfield, Vermont: VARIORUM, Ashgate Publishing.
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| *Straffin, Philip D., Jr. "Liu Hui and the First Golden Age of Chinese Mathematics," ''Mathematics Magazine'', Vol. 71, No. 3 (Jun., 1998): 163-181.
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| *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.
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| *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.
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| *Wilson, Robin J. (2001). ''Stamping Through Mathematics''. New York: Springer-Verlag New York, Inc.
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| {{Inventions}}
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| [[Category:Science and technology in China]]
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| [[Category:China-related lists|Discoveries]]
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| [[Category:Lists of inventions or discoveries|China]]
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| [[Category:History of science and technology in China|Discoveries]]
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