|
Chronology Of Computation Of π
The table below is a brief chronology of computed numerical values of, or bounds on, the mathematical constant pi (). For more detailed explanations for some of these calculations, see Approximations of . The last 100 decimal digits of the latest 2022 world record computation are: 4658718895 1242883556 4671544483 9873493812 1206904813 2656719174 5255431487 2142102057 7077336434 3095295560 Before 1400 1400–1949 1949–2009 2009–present See also * History of pi *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 ... References External links * Borwein, Jonathan,The Life of Pi {{DEFAULTSORT:Chronology Of Computation Of Pi Pi History of mathematics Pi Pi algorithms ... [...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] |
Mahabharata
The ''Mahābhārata'' ( ; sa, महाभारतम्, ', ) is one of the two major Sanskrit epics of ancient India in Hinduism, the other being the ''Rāmāyaṇa''. It narrates the struggle between two groups of cousins in the Kurukshetra War and the fates of the Kaurava and the Pāṇḍava princes and their successors. It also contains philosophical and devotional material, such as a discussion of the four "goals of life" or ''puruṣārtha'' (12.161). Among the principal works and stories in the ''Mahābhārata'' are the '' Bhagavad Gita'', the story of Damayanti, the story of Shakuntala, the story of Pururava and Urvashi, the story of Savitri and Satyavan, the story of Kacha and Devayani, the story of Rishyasringa and an abbreviated version of the ''Rāmāyaṇa'', often considered as works in their own right. Traditionally, the authorship of the ''Mahābhārata'' is attributed to Vyāsa. There have been many attempts to unravel its historical growth and c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aryabhata
Aryabhata (ISO: ) or Aryabhata I (476–550 CE) was an Indian mathematician and astronomer of the classical age of Indian mathematics and Indian astronomy. He flourished in the Gupta Era and produced works such as the ''Aryabhatiya'' (which mentions that in 3600 ''Kali Yuga'', 499 CE, he was 23 years old) and the ''Arya-siddhanta.'' Aryabhata created a system of phonemic number notation in which numbers were represented by consonant-vowel monosyllables. Later commentators such as Brahmagupta divide his work into ''Ganita ("Mathematics"), Kalakriya ("Calculations on Time") and Golapada ("Spherical Astronomy")''. His pure mathematics discusses topics such as determination of square and cube roots, geometrical figures with their properties and mensuration, arithmetric progression problems on the shadow of the gnomon, quadratic equations, linear and indeterminate equations. Aryabhata calculated the value of pi (''π)'' to the fourth decimal digit and was likely aware that p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
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] |
Wang Fan
Wang Fan (228–266), courtesy name Yongyuan, was a Chinese astronomer, mathematician, politician, and writer of the state of Eastern Wu during the Three Kingdoms period of China. Life Wang Fan was from Lujiang Commandery (), which is located southwest of present-day Lujiang County, Anhui. He started his career in Wu as a Gentleman of Writing () during the reign of the first Wu emperor Sun Quan or second Wu emperor Sun Liang, but was dismissed from office. During the reign of the third Wu emperor Sun Xiu, Wang Fan served as a Central Regular Mounted Attendant () alongside He Shao, Xue Ying and Yu Si, and was given an additional appointment as a Chief Commandant of Escorting Cavalry (). He received much praise from his contemporaries. When the Wu government sent him as an ambassador to Wu's ally state, Shu, he was also highly regarded by the Shu government. Upon returning to Wu, he served as a military supervisor at the Wu military garrison in Xiakou (). During the reign of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ptolemy
Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importance to later Byzantine, Islamic, and Western European science. The first is the astronomical treatise now known as the '' Almagest'', although it was originally entitled the ''Mathēmatikē Syntaxis'' or ''Mathematical Treatise'', and later known as ''The Greatest Treatise''. The second is the ''Geography'', which is a thorough discussion on maps and the geographic knowledge of the Greco-Roman world. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. This is sometimes known as the ''Apotelesmatika'' (lit. "On the Effects") but more commonly known as the '' Tetrábiblos'', from the Koine Greek meaning "Four Books", or by its Latin equivalent ''Quadrip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Book Of The Later Han
The ''Book of the Later Han'', also known as the ''History of the Later Han'' and by its Chinese name ''Hou Hanshu'' (), is one of the Twenty-Four Histories and covers the history of the Han dynasty from 6 to 189 CE, a period known as the Later or Eastern Han. The book was compiled by Fan Ye and others in the 5th century during the Liu Song dynasty, using a number of earlier histories and documents as sources. Background In 23 CE, Han dynasty official Wang Mang was overthrown by a peasants' revolt known as the Red Eyebrows. His fall separates the Early (or Western) Han Dynasty from the Later (or Eastern) Han Dynasty. As an orthodox history, the book is unusual in being completed over two hundred years after the fall of the dynasty. Fan Ye's primary source was the ''Dongguan Han Ji'' (東觀漢記; "Han Records of the Eastern Lodge"), which was written during the Han dynasty itself. Contents References Citations Sources ; General * Chavannes, Édouard (1906).T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zhang Heng
Zhang Heng (; AD 78–139), formerly romanized as Chang Heng, was a Chinese polymathic scientist and statesman who lived during the Han dynasty. Educated in the capital cities of Luoyang and Chang'an, he achieved success as an astronomer, mathematician, seismologist, hydraulic engineer, inventor, geographer, cartographer, ethnographer, artist, poet, philosopher, politician, and literary scholar. Zhang Heng began his career as a minor civil servant in Nanyang. Eventually, he became Chief Astronomer, Prefect of the Majors for Official Carriages, and then Palace Attendant at the imperial court. His uncompromising stance on historical and calendrical issues led to his becoming a controversial figure, preventing him from rising to the status of Grand Historian. His political rivalry with the palace eunuchs during the reign of Emperor Shun (r. 125–144) led to his decision to retire from the central court to serve as an administrator of Hejian Kingdom in present-day Hebei. Z ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jialiang
Jialiang () is an ancient Chinese device for measuring several volume standards. The term jialiang is mentioned in the '' Rites of Zhou''. The passage describes the construction of one that includes three measures, ''fu'' (釜), ''dou'' (豆), and ''sheng'' (升); furthermore, the instrument weighs one ''jun'' (鈞) and its sound is the ''gong'' of ''huangzhong'' (黃鐘之宮). Known jialiang give standards for the five measures yue (龠), ge (合, equal to two yue), sheng (升, equal to ten he), dou (斗, equal to ten sheng), and hu (斛, equal to ten dou). The earliest known jialiang was made in the first year of Wang Mang's short-lived Xin Dynasty (9-23 CE), in order to standardize the measurements across the empire. Wang chose bronze to emphasize that it would last and remain as a reference. A 216-character inscription records the process of the casting and shows where each of the five measurements can be found. Wang Mang's jialiang is now in the National Palace Museum, T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
