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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 Heng (78–139) rendered it as 3.1724 (from the proportion of the celestial circle to the diameter of the earth, ) or as \pi \approx \sqrt \approx 3.162. Liu Hui was not satisfied with this value. He commented that it was too large and overshot the mark. Another mathematician Wang Fan (219–257) provided . All these empirical values were accurate to two digits (i.e. one decimal place). Liu Hui was the first Chinese mathematician to provide a rigorous algorithm for calculation of to any accuracy. Liu Hui's own calculation with a 96-gon provided an accuracy of five digits: . Liu Hui remarked in his commentary to ''The Nine Chapters on the Mathematical Art'', that the ratio of the circumference of an inscribed hexagon to the diamete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rod Calculus
Rod calculus or rod calculation was the mechanical method of algorithmic computation with counting rods in China from the Warring States to Ming dynasty before the counting rods were increasingly replaced by the more convenient and faster abacus. Rod calculus played a key role in the development of Chinese mathematics to its height in Song Dynasty and Yuan Dynasty, culminating in the invention of polynomial equations of up to four unknowns in the work of Zhu Shijie. Hardware The basic equipment for carrying out rod calculus is a bundle of counting rods and a counting board. The counting rods are usually made of bamboo sticks, about 12 cm- 15 cm in length, 2mm to 4 mm diameter, sometimes from animal bones, or ivory and jade (for well-heeled merchants). A counting board could be a table top, a wooden board with or without grid, on the floor or on sand. In 1971 Chinese archaeologists unearthed a bundle of well-preserved animal bone counting rods stored in a silk pouch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pi Algorithms
The number (; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number appears in many formulas across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as \tfrac are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an equation involving only sums, products, powers, and integers. The transcendence of implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. The decimal digits of appear to be randomly distributed, but no proof of this conjecture has been found. For thousands of years, mathematicians have attempted to extend their understanding of , sometimes by computing i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Method Of Exhaustion
The method of exhaustion (; ) is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape. If the sequence is correctly constructed, the difference in area between the ''n''th polygon and the containing shape will become arbitrarily small as ''n'' becomes large. As this difference becomes arbitrarily small, the possible values for the area of the shape are systematically "exhausted" by the lower bound areas successively established by the sequence members. The method of exhaustion typically required a form of proof by contradiction, known as ''reductio ad absurdum''. This amounts to finding an area of a region by first comparing it to the area of a second region, which can be "exhausted" so that its area becomes arbitrarily close to the true area. The proof involves assuming that the true area is greater than the second area, proving that assertion false, assuming it is less than the second area ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adriaan Anthonisz
Adriaan Anthonisz (also known as Adriaen Anthonisz of Alcmaer) (1527–1607) was a Dutch mathematician, Surveying, surveyor, cartographer, and military engineer who specialized in the design of fortifications. As a mathematician Anthonisz calculated in 1585 the ratio of a circle's circumference to its diameter, which would later be called pi. Life Anthonisz served as burgomaster (mayor) of Alkmaar in the Netherlands from 1582. Adriaan fathered two sons, and named them both Metius (from the Dutch word ''meten'', meaning 'measuring', 'measurer', or surveyor). They each became prominent members of society. Adriaan Metius (9 Dec 1571 – 6 Sep 1635) was a Dutch geometer and astronomer. Jacob Metius worked as an instrument-maker and a specialist in grinding lenses and applied for patent rights for the telescope a few weeks after Middelburg spectacle-maker Hans Lippershey tried to patent the same device. Career In 1585 Anthonisz discovered that the ratio of a circle's circumference to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zhao Youqin's π Algorithm
Zhao Youqin's algorithm was an algorithm devised by Yuan dynasty Chinese astronomer and mathematician Zhao Youqin (, ? – 1330) to calculate the value of in his book ''Ge Xiang Xin Shu'' (). Algorithm Zhao Youqin started with an inscribed square in a circle with radius r. If \ell denotes the length of a side of the square, draw a perpendicular In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the ''perpendicular symbol'', ⟂. It ca ... line d from the center of the circle to side l. Let e denotes r − d. Then from the diagram: :d=\sqrt :e=r-d=r-\sqrt. Extend the perpendicular line d to dissect the circle into an octagon; \ell_2 denotes the length of one side of octagon. :\ell_2=\sqrt :\ell_2=\frac\sqrt Let l_3 denotes the length of a side of hexadecagon :\ell_3=\frac\sqrt similarly :\ell ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yuan Dynasty
The Yuan dynasty (), officially the Great Yuan (; xng, , , literally "Great Yuan State"), was a Mongol-led imperial dynasty of China and a successor state to the Mongol Empire after its division. It was established by Kublai, the fifth khagan-emperor of the Mongol Empire from the Borjigin clan, and lasted from 1271 to 1368. In orthodox Chinese historiography, the Yuan dynasty followed the Song dynasty and preceded the Ming dynasty. Although Genghis Khan had been enthroned with the Han-style title of Emperor in 1206 and the Mongol Empire had ruled territories including modern-day northern China for decades, it was not until 1271 that Kublai Khan officially proclaimed the dynasty in the traditional Han style, and the conquest was not complete until 1279 when the Southern Song dynasty was defeated in the Battle of Yamen. His realm was, by this point, isolated from the other Mongol-led khanates and controlled most of modern-day China and its surrounding areas, including ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Qin Jiushao
Qin Jiushao (, ca. 1202–1261), courtesy name Daogu (道古), 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 gauge instrument used to gather meteorological data. Biography Although Qin Jiushao was born in Ziyang, Sichuan, his family came from Shandong province. He is regarded as one of the greatest mathematicians in Chinese history. This is especially remarkable because Qin did not devote his life to mathematics. He was accomplished in many other fields and held a series of bureaucratic positions in several Chinese provinces. Qin wrote ''Shùshū Jiǔzhāng'' (“Mathematical Treatise in Nine Sections”) in 1247 CE. This treatise covered a variety of topics including indeterminate equations and the numerical solution of certain polynomial equations up to 10th order, as well as discussions on military matters and surveying. In the treatise Qin in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
He Chengtian
He or HE may refer to: Language * He (pronoun), an English pronoun * He (kana), the romanization of the Japanese kana へ * He (letter), the fifth letter of many Semitic alphabets * He (Cyrillic), a letter of the Cyrillic script called ''He'' in Ukrainian * Hebrew language (ISO 639-1 code: he) Places * He County, Anhui, China * He River, or Hejiang (贺江), a tributary of the Xi River in Guangxi and Guangdong * Hebei, abbreviated as ''HE'', a province of China (Guobiao abbreviation HE) * Hesse, abbreviated as ''HE'', a state of Germany People * He (surname), Chinese surname, sometimes transcribed Hé or Ho; includes a list of notable individuals so named * Zheng He (1371–1433), Chinese admiral * He (和) and He (合), collectively known as 和合二仙 ('' He-He er xian'', "Two immortals He"), two Taoist immortals known as the "Immortals of Harmony and Unity" * Immortal Woman He, or He Xiangu, one of the Eight Immortals of Taoism Arts, entertainment, and media * "He" ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 3.1415927, a record in accuracy which would not be surpassed for over 800 years. Life and works Chongzhi's ancestry was from modern Baoding, Hebei. To flee from the ravages of war, Zu's grandfather Zu Chang moved to the Yangtze, as part of the massive population movement during the Eastern Jin. Zu Chang () at one point held the position of Chief Minister for the Palace Buildings () within the Liu Song and was in charge of government construction projects. Zu's father, Zu Shuozhi (), also served the court and was greatly respected for his erudition. Zu was born in Jiankang. His family had historically been involved in astronomical research, and from childhood Zu was exposed to both astronomy and mathematics. When he was only a youth his tal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph Needham
Noel Joseph Terence Montgomery Needham (; 9 December 1900 – 24 March 1995) was a British biochemist, historian of science and sinologist known for his scientific research and writing on the history of Chinese science and technology, initiating publication of the multivolume ''Science and Civilisation in China''. He was elected a fellow of the Royal Society in 1941 and a fellow of the British Academy in 1971. In 1992, Queen Elizabeth II conferred on him the Companionship of Honour, and the Royal Society noted he was the only living person to hold these three titles. Early life Needham's father, Joseph was a doctor, and his mother, Alicia Adelaïde, née Montgomery (1863–1945), was a music composer from Oldcastle, County Meath, Ireland. His father, born in East London, then a poor section of town, rose to became a Harley Street physician, but frequently battled with Needham's mother. The young Needham often mediated. In his early teens, he was taken to hear the Sun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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