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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] |
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] |
Simple Continued Fraction
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 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] |
History Of Mathematics
The history of mathematics deals with the origin of discoveries in mathematics and the History of mathematical notation, mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad (region), Akkad and Assyria, followed closely by Ancient Egypt and the Levantine state of Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the field of astronomy to record time and formulate calendars. The earliest mathematical texts available are from Mesopotamia and Ancient Egypt, Egypt – ''Plimpton 322'' (Babylonian mathematics, Babylonian – 1900 BC),Friberg, J. (1981). "Methods and traditions of Babylonian mathematics. Plimpton 322, Pythagorean triples, and the Babylonian triangle parameter equations", ''Historia Mathematica'', 8, pp. 277–318. the ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ie . 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 diamet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rational Number
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (for example, The set of all rational numbers is often referred to as "the rationals", and is closed under addition, subtraction, multiplication, and division by a nonzero rational number. It is a field under these operations and therefore also called the field of rationals or the field of rational numbers. It is usually denoted by boldface , or blackboard bold A rational number is a real number. The real numbers that are rational are those whose decimal expansion either terminates after a finite number of digits (example: ), or eventually begins to repeat the same finite sequence of digits over and over (example: ). This statement is true not only in base 10, but also in every other integer base, such as the binary and hexadecimal ones (see ). A real n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
He Chengtian
He or HE may refer to: Language * He (letter), the fifth letter of the Semitic abjads * He (pronoun), a pronoun in Modern English * He (kana), one of the Japanese kana (へ in hiragana and ヘ in katakana) * Ge (Cyrillic), a Cyrillic letter called ''He'' in Ukrainian * Hebrew language (ISO 639-1 language 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) * Hessen, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pi Approximation Day
Pi Day is an annual celebration of the mathematical constant (pi). Pi Day is observed on March 14 (the 3rd month) since 3, 1, and 4 are the first three significant figures of , and was first celebrated in the United States. It was founded in 1988 by Larry Shaw, an employee of a science museum in San Francisco, the Exploratorium. Celebrations often involve eating pie or holding pi recitation competitions. In 2009, the United States House of Representatives supported the designation of Pi Day.United States. Cong. House. Supporting the designation of Pi Day, and for other purposes. 111th CongLibrary of Congress UNESCO's 40th General Conference designated Pi Day as the International Day of Mathematics in November 2019. Other dates when people celebrate pi include Pi Approximation Day on July 22 (22/7 in the ''day/month'' format), another approximation of ; and June 28 (6.28), an approximation of 2 or (tau). History In 1988, the earliest known official or large-scale ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Science And Technology In China
Ancient Han Chinese, Chinese scientists and engineers made significant scientific innovations, findings and technological advances across various scientific disciplines including the natural sciences, engineering, medicine, military technology, mathematics, geology and astronomy. Among the earliest List of Chinese inventions, inventions were the abacus, the sundial, and the Kongming lantern. The ''Four Great Inventions'' – the compass, gunpowder, papermaking, and printing – were among the most important technological advances, only known to Europe by the end of the Middle Ages 1000 years later. The Tang dynasty (AD 618–906) in particular was a time of great innovation. A good deal of exchange occurred between Western and List of Chinese discoveries, Chinese discoveries up to the Qing dynasty. The Jesuit China missions of the 16th and 17th centuries introduced Western science and astronomy, while undergoing its own Scientific Revolution, scientific revolution, at the same ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chinese Mathematical Discoveries
Chinese may refer to: * Something related to China * Chinese people, people identified with China, through nationality, citizenship, and/or ethnicity **Han Chinese, East Asian ethnic group native to China. **''Zhonghua minzu'', the supra-ethnic concept of the Chinese nation ** List of ethnic groups in China, people of various ethnicities in contemporary China ** Ethnic minorities in China, people of non-Han Chinese ethnicities in modern China ** Ethnic groups in Chinese history, people of various ethnicities in historical China ** Nationals of the People's Republic of China ** Nationals of the Republic of China ** Overseas Chinese, Chinese people residing outside the territories of mainland China, Hong Kong, Macau, and Taiwan * Sinitic languages, the major branch of the Sino-Tibetan language family ** Chinese language, a group of related languages spoken predominantly in China, sharing a written script (Chinese characters in traditional and simplified forms) *** Standard Chines ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
