|
Zu Chongzhi
Zu Chongzhi (; 429 – 500), courtesy name Wenyuan (), was a Chinese astronomer, inventor, mathematician, politician, 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 precision which would not be surpassed for nearly 900 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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zu (surname)
Zu is the Mandarin pinyin romanization of the Chinese surname written in Chinese character. It is romanized Tsu in Wade–Giles. It is listed 249th in the Song dynasty classic text ''Hundred Family Surnames''. It is not among the 300 most common surnames in China. Notable people * Zu Ti ( 祖逖; 266–321), celebrated Eastern Jin general * Zu Yue ( 祖約; died 330), Eastern Jin general, younger brother of Zu Ti * Zu Chongzhi (429–500), Liu Song dynasty mathematician and astronomer * Zu Gengzhi (450? – 520?), mathematician, son of Zu Chongzhi * Zu Ting (6th century), scholar-official of the Northern Qi dynasty * Zu Xiaosun (6th – 7th century), Sui and Tang dynasty musician * Zu Yong (699–746?), Tang dynasty poet * Zu Dashou (died 1656), Ming dynasty general who surrendered to the Qing * Zu Zhiwang ( 祖之望; 1754–1813), Qing dynasty Governor of Hunan and Shandong Shandong is a coastal Provinces of China, province in East China. Shandong has played a maj ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lunar Month
In lunar calendars, a lunar month is the time between two successive syzygies of the same type: new moons or full moons. The precise definition varies, especially for the beginning of the month. Variations In Shona, Middle Eastern, and European traditions, the month starts when the young crescent moon first becomes visible, at evening, after conjunction with the Sun one or two days before that evening (e.g., in the Islamic calendar). In ancient Egypt, the lunar month began on the day when the waning moon could no longer be seen just before sunrise. Others run from full moon to full moon. Yet others use calculation, of varying degrees of sophistication, for example, the Hebrew calendar, the Chinese calendar, or the ecclesiastical lunar calendar. Calendars count integer days, so months may be 29 or 30 days in length, in some regular or irregular sequence. Lunar cycles are prominent, and calculated with great precision in the ancient Hindu Panchangam calendar, widely us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Best Rational Approximation
A simple or regular continued fraction is a continued fraction with numerators all equal one, and denominators built from a sequence \ of integer numbers. The sequence can be finite or infinite, resulting in a finite (or terminated) continued fraction like :a_0 + \cfrac or an infinite continued fraction like :a_0 + \cfrac Typically, such a continued fraction is obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on. In the ''finite'' case, the iteration/recursion is stopped after finitely many steps by using an integer in lieu of another continued fraction. In contrast, an ''infinite'' continued fraction is an infinite expression. In either case, all integers in the sequence, other than the first, must be positive. The integers a_i are called the coefficients or terms of the continued fraction. Simple contin ... [...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, 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 its diamet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Netherlands
, Terminology of the Low Countries, informally Holland, is a country in Northwestern Europe, with Caribbean Netherlands, overseas territories in the Caribbean. It is the largest of the four constituent countries of the Kingdom of the Netherlands. The Netherlands consists of Provinces of the Netherlands, twelve provinces; it borders Germany to the east and Belgium to the south, with a North Sea coastline to the north and west. It shares Maritime boundary, maritime borders with the United Kingdom, Germany, and Belgium. The official language is Dutch language, Dutch, with West Frisian language, West Frisian as a secondary official language in the province of Friesland. Dutch, English_language, English, and Papiamento are official in the Caribbean Netherlands, Caribbean territories. The people who are from the Netherlands is often referred to as Dutch people, Dutch Ethnicity, Ethnicity group, not to be confused by the language. ''Netherlands'' literally means "lower countries" i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedes
Archimedes of Syracuse ( ; ) was an Ancient Greece, Ancient Greek Greek mathematics, mathematician, physicist, engineer, astronomer, and Invention, inventor from the ancient city of Syracuse, Sicily, Syracuse in History of Greek and Hellenistic Sicily, Sicily. Although few details of his life are known, based on his surviving work, he is considered one of the leading scientists in classical antiquity, and one of the greatest mathematicians of all time. Archimedes anticipated modern calculus and mathematical analysis, analysis by applying the concept of the Cavalieri's principle, infinitesimals and the method of exhaustion to derive and rigorously prove many geometry, geometrical theorem, theorems, including the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral. Archimedes' other math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yoshio Mikami
was a Japanese mathematician and historian of ''Japanese mathematics''. He was born February 16, 1875, in Kotachi, Hiroshima prefecture. He attended the High School of Tohoku University, and in 1911 was admitted to the Imperial University of Tokyo. He studied history of Japanese and Chinese mathematics. In 1913, he published "The Development of Mathematics in China and Japan" in Leipzig.Yoshio Mikami, The Development of Mathematics in China and Japan, 1913, Library of Congress 61-13497 This book consisted of two parts with 47 chapters. Part one has 21 chapters that describe in depth several important Chinese mathematicians and mathematical classics including Liu Hui, Shen Kuo, Qin Jiushao, Sun Tzu (mathematician), Sun Tzu, The Nine Chapters on the Mathematical Art, Mathematical Treatise in Nine Sections, Li Zhi (mathematician), Li Ye, Zhu Shijie and study on π. Part II deals with important ''wasan'' mathematicians and their works, including Kambei Mori, Yoshida Koyu, Kowa Seki, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Counting Rods
Counting rods (筭) are small bars, typically 3–14 cm (1" to 6") long, that were used by mathematicians for calculation in ancient East Asia. They are placed either horizontally or vertically to represent any integer or rational number. The written forms based on them are called rod numerals. They are a true Positional notation, positional numeral system with numerical digit, digits for 1–9 and a blank for 0, from the Warring States period, Warring states period (circa 475 BCE) to the 16th century. History Chinese arithmeticians used counting rods well over two thousand years ago. In 1954, forty-odd counting rods of the Warring States period (5th century BCE to 221 BCE) were found in Zuǒjiāgōngshān (左家公山) Chu (state), Chu Grave No.15 in Changsha, Hunan. In 1973, archeologists unearthed a number of wood scripts from a tomb in Hubei dating from the period of the Han dynasty (206 BCE to 220 CE). On one of the wooden scripts was written: "当利二月定算� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof That 22/7 Exceeds π
Proofs of the mathematical result that the rational number is greater than (pi) date back to antiquity. One of these proofs, more recently developed but requiring only elementary techniques from calculus, has attracted attention in modern mathematics due to its mathematical elegance and its connections to the theory of Diophantine approximations. Stephen Lucas calls this proof "one of the more beautiful results related to approximating ". Julian Havil ends a discussion of continued fraction approximations of with the result, describing it as "impossible to resist mentioning" in that context. The purpose of the proof is not primarily to convince its readers that is indeed bigger than . Systematic methods of computing the value of exist. If one knows that is approximately 3.14159, then it trivially follows that < , which is approximately 3.142857. But it takes much less work to show that < by the method used in this proof than to show that is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Milü
''Milü'' (), also known as Zulü (Zu's ratio), is the name given to an approximation of ( pi) found by the Chinese mathematician and astronomer Zu Chongzhi during the 5th century. Using Liu Hui's algorithm, which is based on the areas of regular polygons approximating a circle, Zu computed as being between 3.1415926 and 3.1415927 and gave two rational approximations of , and , which were named ''yuelü'' () and ''milü'' respectively. is the best rational approximation of with a denominator of four digits or fewer, being accurate to six decimal places. It is within % of the value of , or in terms of common fractions overestimates by less than . The next rational number (ordered by size of denominator) that is a better rational approximation of is , though it is still only correct to six decimal places. To be accurate to seven decimal places, one needs to go as far as . For eight, is needed. The accuracy of ''milü'' to the true value of can be explained using the co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Approximations Of π
Approximation#Mathematics, Approximations for the mathematical constant pi () in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning of the Common Era. In Chinese mathematics, this was improved to approximations correct to what corresponds to about seven decimal digits by the 5th century. Further progress was not made until the 14th century, when Madhava of Sangamagrama developed approximations correct to eleven and then thirteen digits. Jamshīd al-Kāshī achieved sixteen digits next. Early modern mathematicians reached an accuracy of 35 digits by the beginning of the 17th century (Ludolph van Ceulen), and 126 digits by the 19th century (Jurij Vega). The record of manual approximation of is held by William Shanks, who calculated 527 decimals correctly in 1853. Since the middle of the 20th century, the approximation of has been the task of electronic digital computers (for a comprehensive account, see chronology of computation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
