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Milü
Milü (; "close ratio"), also known as Zulü ( Zu's ratio), is the name given to an approximation to (pi) found by Chinese mathematician and astronomer Zu Chongzhi in the 5th century. Using Liu Hui's algorithm (which is based on the areas of regular polygons approximating a circle), Zu famously computed to be between 3.1415926 and 3.1415927 and gave two rational approximations of , and , naming them respectively Yuelü (; "approximate ratio") and Milü. 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 , still only correct to six decimal places and hardly closer to than . 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 ca ... [...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] |
Approximations Of π
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 15th century (through the efforts of Jamshīd al-Kāshī). 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), surpassing the accuracy required for any conceivable application outside of pure mathematics. The record of manual approximation of is held by William Shanks, who calculated 527 digits 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 of ). On June 8, 2022, the current r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continued Fraction
In mathematics, a continued fraction is an expression (mathematics), expression obtained through an iterative process of representing a number as the sum of its integer part and the multiplicative inverse, reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on. In a finite continued fraction (or terminated continued fraction), the iteration/recursion is terminated after finitely many steps by using an integer in lieu of another continued fraction. In contrast, an infinite continued fraction is an infinite expression (mathematics), infinite expression. In either case, all integers in the sequence, other than the first, must be positive number, positive. The integers a_i are called the coefficients or terms of the continued fraction. It is generally assumed that the numerator of all of the fractions is 1. If arbitrary values and/or function (mathematics), functions are used in place of one or more of the numerat ... [...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 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 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 patterns in nature, the field of astronomy and to record time and formulate calendars. The earliest mathematical texts available are from Mesopotamia and Egypt – '' Plimpton 322'' ( Babylonian c. 2000 – 1900 BC), the ''Rhind Mathematical Papyrus'' ( Egyptian c. 1800 BC) and the '' Moscow Mathematical Papyrus'' (Egyptian c. 1890 BC). All of these texts mention the so-called Pythagorean triples, so, by inference, the Pythagorean theorem seems to be the most anci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chinese Words And Phrases
Chinese can refer to: * Something related to China * Chinese people, people of Chinese nationality, citizenship, and/or ethnicity **''Zhonghua minzu'', the supra-ethnic concept of the Chinese nation ** List of ethnic groups in China, people of various ethnicities in contemporary China ** Han Chinese, the largest ethnic group in the world and the majority ethnic group in Mainland China, Hong Kong, Macau, Taiwan, and Singapore ** 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 c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chinese Mathematical Discoveries
Chinese can refer to: * Something related to China * Chinese people, people of Chinese nationality, citizenship, and/or ethnicity **''Zhonghua minzu'', the supra-ethnic concept of the Chinese nation ** List of ethnic groups in China, people of various ethnicities in contemporary China ** Han Chinese, the largest ethnic group in the world and the majority ethnic group in Mainland China, Hong Kong, Macau, Taiwan, and Singapore ** 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 (Chi ... [...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 (3/14 in the ''month/day'' format) since 3, 1, and 4 are the first three significant figures of . It was founded in 1988 by Larry Shaw, an employee of the San Francisco, California science museum, 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. Alternative dates for the holiday include July 2222 July in the ''day/month'' format (22/7, an approximation of ) and June 28 (6.28, an approximation of 2 or tau). History In 1988, the earliest known official or large-scale celebration of Pi Day was organized by Larry Shaw ... [...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] |
Odd Numbers
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is a multiple of two, and odd if it is not.. For example, −4, 0, 82 are even because \begin -2 \cdot 2 &= -4 \\ 0 \cdot 2 &= 0 \\ 41 \cdot 2 &= 82 \end By contrast, −3, 5, 7, 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers like 1/2 or 4.201. See the section "Higher mathematics" below for some extensions of the notion of parity to a larger class of "numbers" or in other more general settings. Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
