# Category:Ancient Chinese mathematicians

## Pages in category "Ancient Chinese mathematicians"

The following 10 pages are in this category, out of 10 total. This list may not reflect recent changes (learn more).

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## Pages in category "Ancient Chinese mathematicians"

The following 10 pages are in this category, out of 10 total. This list may not reflect recent changes (learn more).

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1. Cai Yong – Cai Yong courtesy name Bojie was a scholar of the Eastern Han Dynasty. He was well-versed in calligraphy, music, mathematics and astronomy, One of his daughters was the famous Cai Wenji. Cai Yong was born into a local family in Chenliu. When his father Cai Leng died, Cai Yong lived with his uncle Cai Zhi while taking care for his own mother for her last three years. When she died, Cai Yong became known for his arrangement of his mothers tomb, after that, Cai Yong studied composition, mathematics, astronomy, pitch-pipes, and music under Hu Guang, one of the highest-ranking officials in the Han court. In the early 160s Cai Yong was recommended to the Emperor Huan by the senior eunuchs for his skill with the drums, on his way to the capital, Cai Yong feigned illness to return home to study in seclusion. Ten years later in the early 170s, Cai Yong went to serve Qiao Xuan as a clerk, afterwards, Cai Yong served as a county magistrate and then a Consultant in the capital, in charge of editing and collating the text in the library. Known for his skills, he was constantly commissioned to write eulogies, memorial inscriptions. In 175, in fear of trying to alter the Confucian classics to support their views, Cai Yong. Emperor Ling approved, and the result was the Xiping Stone Classics, completed in 183, throughout his political career, he was an advocate of restoring ceremonial practices and often criticized against the eunuchs influence in politics. He was successful in persuading the emperor to participate in a ritual in the winter of 177 through his memorials, in the autumn of 178, the scholars were asked for advice on recent ill omens. Cai Yong responded with criticisms of eunuch pretensions, the eunuchs learnt of the attack, and accused Cai Yong and his uncle Cai Zhi of extortion. They were thrown into prison and sentenced to death, but the sentence was remitted to exile in the northern frontiers. Nine months later, he cited to the throne that his work on the history and classics were at risk from enemy raids. However, he offended the sibling of an influential eunuch during a banquet before his return. Cai Yong fled south to the Wu and Guiji commanderies and stayed there for twelve years, when Dong Zhuo came to power in 189, he summoned Cai Yong back to the capital. At first Cai Yong was unwilling, but Dong Zhuo enforced his demand with the threat I can eliminate whole clans, Cai Yong had no choice but to comply. Under Dong Zhuo, Cai Yong was made a General of the Household, in 192, when Dong Zhuo was killed in a plot by Wang Yun, Cai Yong was put into prison and sentenced to death for allegedly expressing grief at Dong Zhuos death

2. Liu Hui – Liu Hui was an Ancient Chinese mathematician. He lived in the state of Cao Wei during the Three Kingdoms period of Chinese history, in 263, he edited and published a book with solutions to mathematical problems presented in the famous Chinese book of mathematics known as The Nine Chapters on the Mathematical Art. He was a descendant of the Marquis of Zixiang of the Han dynasty and he completed his commentary to the Nine Chapters in the year 263. He probably visited Luoyang, and measured the suns shadow, along with Zu Chongzhi, Liu Hui was known as one of the greatest mathematicians of ancient China. Liu Hui expressed all of his results in the form of decimal fractions. Liu provided commentary on a proof of a theorem identical to the Pythagorean theorem. In the field of plane areas and solid figures, Liu Hui was one of the greatest contributors to empirical solid geometry, for example, he found that a wedge with rectangular base and both sides sloping could be broken down into a pyramid and a tetrahedral wedge. He also found that a wedge with trapezoid base and both sides sloping could be made to give two tetrahedral wedges separated by a pyramid, in his commentaries on the Nine Chapters, he presented, An algorithm for calculation of pi in the comments to chapter 1. He calculated pi to 3.141024 < π <3.142074 with a 192 sided polygon, Archimedes used a circumscribed 96-polygon to obtain the inequality π <227, and then used an inscribed 96-gon to obtain the inequality 22371 < π. Liu Hui used only one inscribed 96-gon to obtain his π inequality, but he commented that 3.142074 was too large, and picked the first three digits of π =3.141024 ~3.14 and put it in fraction form π =15750. He later invented a method and obtained π =3.1416. Nine Chapters had used the value 3 for π, but Zhang Heng had previously estimated pi to the root of 10. Cavalieris principle to find the volume of a cylinder and the intersection of two perpendicular cylinders although this work was finished by Zu Chongzhi and Zu Gengzhi. Lius commentaries often include explanations why some methods work and why others do not, although his commentary was a great contribution, some answers had slight errors which was later corrected by the Tang mathematician and Taoist believer Li Chunfeng. Liu Hui also presented, in an appendix of 263 AD called Haidao Suanjing or The Sea Island Mathematical Manual, several problems related to surveying. This book contained many practical problems of geometry, including the measurement of the heights of Chinese pagoda towers and this smaller work outlined instructions on how to measure distances and heights with tall surveyors poles and horizontal bars fixed at right angles to them. Liu Huis information about surveying was known to his contemporaries as well, the cartographer and state minister Pei Xiu outlined the advancements of cartography, surveying, and mathematics up until his time. This included the first use of a grid and graduated scale for accurate measurement of distances on representative terrain maps

3. Zhang Heng – Zhang Heng, formerly romanized as Chang Heng, was a Han Chinese polymath from Nanyang who lived during the Han dynasty. Zhang Heng began his career as a civil servant in Nanyang. Eventually, he became Chief Astronomer, Prefect of the Majors for Official Carriages and 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 led to his decision to retire from the court to serve as an administrator of Hejian in Hebei. Zhang returned home to Nanyang for a time, before being recalled to serve in the capital once more in 138. He died there a year later, in 139, Zhang applied his extensive knowledge of mechanics and gears in several of his inventions. He improved previous Chinese calculations for pi and his fu and shi poetry were renowned in his time and studied and analyzed by later Chinese writers. Zhang received many honors for his scholarship and ingenuity, some modern scholars have compared his work in astronomy to that of the Greco-Roman Ptolemy. Born in the town of Xie in Nanyang Commandery, Zhang Heng came from a distinguished, at age ten, Zhangs father died, leaving him in the care of his mother and grandmother. An accomplished writer in his youth, Zhang left home in the year 95 to pursue his studies in the capitals of Changan, while traveling to Luoyang, Zhang passed by a hot spring near Mount Li and dedicated one of his earliest fu poems to it. Government authorities offered Zhang appointments to offices, including a position as one of the Imperial Secretaries, yet he acted modestly. At age twenty-three, he returned home with the title Officer of Merit in Nanyang, serving as the master of documents under the administration of Governor Bao De, as he was charged with composing inscriptions and dirges for the governor, he gained experience in writing official documents. As Officer of Merit in the commandery, he was responsible for local appointments to office. He spent much of his time composing rhapsodies on the capital cities, when Bao De was recalled to the capital in 111 to serve as a minister of finance, Zhang continued his literary work at home in Xie. Zhang Heng began his studies in astronomy at the age of thirty and began publishing his works on astronomy, in 112, Zhang was summoned to the court of Emperor An, who had heard of his expertise in mathematics. When he was nominated to serve at the capital, Zhang was escorted by carriage—a symbol of his official status—to Luoyang and he was promoted to Chief Astronomer for the court, serving his first term from 115–120 under Emperor An and his second under the succeeding emperor from 126–132. As Chief Astronomer, Zhang was a subordinate of the Minister of Ceremonies, when the government official Dan Song proposed the Chinese calendar should be reformed in 123 to adopt certain apocryphal teachings, Zhang opposed the idea. He considered the teachings to be of questionable stature and believed they could introduce errors, others shared Zhangs opinion and the calendar was not altered, yet Zhangs proposal that apocryphal writings should be banned was rejected

4. Zu Chongzhi – Zu Chongzhi, courtesy name Wenyuan, was a prominent Chinese mathematician and astronomer during the Liu Song and Southern Qi Dynasties. Chongzhis ancestry was from modern Baoding, Hebei, to flee from the ravage of war, Zus 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, Zus father, Zu Shuozhi also served the court and was greatly respected for his erudition. His family had historically been involved in research, and from childhood Zu was exposed to both astronomy and mathematics. When he was only a youth his talent earned him much repute, when Emperor Xiaowu of Liu Song heard of him, he was sent to an Academy, the Hualin Xuesheng, and later at the Imperial Nanjing University to perform research. In 461 in Nanxu, he was engaged in work at the office of the local governor, Zu Chongzhi, along with his son Zu Gengzhi wrote a mathematical text entitled Zhui Shu. It is said that the treatise contains formulas for the volume of the sphere, cubic equations and this book didnt survive to the present day, it has been lost since the Song Dynasty. His mathematical achievements included, the Daming calendar introduced by him in 465, distinguishing the sidereal year and the tropical year, and he measured 45 years and 11 months per degree between those two, and today we know the difference is 70.7 years per degree. Calculating one year as 365.24281481 days, which is close to 365.24219878 days as we know today. Calculating the Jupiter year as about 11.858 Earth years, deriving two approximations of pi, which held as the most accurate approximation for π for over nine hundred years. His best approximation was between 3.1415926 and 3.1415927, with 355/113 and 22/7 being the other notable approximations and he obtained the result by approximating a circle with a 24,576 sided polygon. Hence Mikami strongly urged that the fraction 355/113 be named after Zu Chongzhi as Zus fraction, in Chinese literature, this fraction is known as Zus ratio. Zus ratio is a best rational approximation to π, and is the closest rational approximation to π from all fractions with denominator less than 16600, finding the volume of a sphere as πD3/6 where D is diameter. Zu was an astronomer who calculated the values of time with unprecedented precision. His methods of interpolating and the use of integration is far ahead of his time, even the astronomer Yi Xings isnt comparable to his value. The Sung dynasty calendar was backwards to the Northern barbarians because they were implementing their daily lives with the Da Ming Li. It is said that his methods of calculation were so advanced, the majority of Zus great mathematical works are recorded in his lost text the Zhui Shu. Most schools argue about his complexity since traditionally the Chinese had developed mathematics as algebraic, logically, scholars assume that the Zhui Shu yields methods of cubic equations