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Zu Chongzhi
Zu Chongzhi (Chinese: 祖沖之; 429 – 500), courtesy name Wenyuan (Chinese: 文遠), 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.
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 (祖昌) at one point held the position of Chief Minister for the Palace Buildings (大匠卿) within the Liu Song and was in charge of government construction projects. Zu's father, Zu Shuozhi (祖朔之), 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 talent earned him much repute. When Emperor Xiaowu of Song heard of him, he was sent to the Hualin Xuesheng (華林學省) academy, and later the Imperial Nanjing University (Zongmingguan) to perform research. In 461 in Nanxu (today Zhenjiang, Jiangsu), he was engaged in work at the office of the local governor. In 464, Zu moved to Louxian (today Songjiang district, Shanghai), there, he compiled the Daming calendar and calculated π.
Zu Chongzhi, along with his son Zu Gengzhi, wrote a mathematical text entitled Zhui Shu (綴述; "Methods for Interpolation"). It is said that the treatise contained formulas for the volume of a sphere, cubic equations and an accurate value of pi. This book has been lost since the Song dynasty.
His mathematical achievements included
Zu was an accomplished astronomer who calculated the time values with unprecedented precision. His methods of interpolation and the use of integration were far ahead of his time. Even the results of the astronomer Yi Xing (who was beginning to utilize foreign knowledge) were not comparable. The Sung dynasty calendar was backwards to the "Northern barbarians" because they were implementing their daily lives with the Da Ming Li.[clarification needed] It is said that his methods of calculation were so advanced, the scholars of the Sung dynasty and Indo influence astronomers of the Tang dynasty found it confusing.
The majority of Zu's 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 and equational. Logically, scholars assume that the Zhui Shu yields methods of cubic equations. His works on the accurate value of pi describe the lengthy calculations involved. Zu used Liu Hui's π algorithm described earlier by Liu Hui to inscribe a 12,288-gon. Zu's value of pi is precise to six decimal places and for almost nine hundred years thereafter no subsequent mathematician computed a value this precise. Zu also worked on deducing the formula for the volume of a sphere with his son Zu Gengzhi. In their calculation, Zu used the concept that two solids with equal cross-sectional areas at equal heights must also have equal volumes to find the volume of a Steinmetz solid. And further multiplied the volume of the Steinmetz solid with π/4, therefore found the volume of a sphere as πd^3/6 (d is the diameter of the sphere).
In 488, Zu Chongzhi was responsible for erecting water powered trip hammer mills which was inspected by Emperor Wu of Southern Qi during the early 490s.
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Zu Chongzhi
Zu Chongzhi (Chinese: 祖沖之; 429 – 500), courtesy name Wenyuan (Chinese: 文遠), 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.
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 (祖昌) at one point held the position of Chief Minister for the Palace Buildings (大匠卿) within the Liu Song and was in charge of government construction projects. Zu's father, Zu Shuozhi (祖朔之), 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 talent earned him much repute. When Emperor Xiaowu of Song heard of him, he was sent to the Hualin Xuesheng (華林學省) academy, and later the Imperial Nanjing University (Zongmingguan) to perform research. In 461 in Nanxu (today Zhenjiang, Jiangsu), he was engaged in work at the office of the local governor. In 464, Zu moved to Louxian (today Songjiang district, Shanghai), there, he compiled the Daming calendar and calculated π.
Zu Chongzhi, along with his son Zu Gengzhi, wrote a mathematical text entitled Zhui Shu (綴述; "Methods for Interpolation"). It is said that the treatise contained formulas for the volume of a sphere, cubic equations and an accurate value of pi. This book has been lost since the Song dynasty.
His mathematical achievements included
Zu was an accomplished astronomer who calculated the time values with unprecedented precision. His methods of interpolation and the use of integration were far ahead of his time. Even the results of the astronomer Yi Xing (who was beginning to utilize foreign knowledge) were not comparable. The Sung dynasty calendar was backwards to the "Northern barbarians" because they were implementing their daily lives with the Da Ming Li.[clarification needed] It is said that his methods of calculation were so advanced, the scholars of the Sung dynasty and Indo influence astronomers of the Tang dynasty found it confusing.
The majority of Zu's 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 and equational. Logically, scholars assume that the Zhui Shu yields methods of cubic equations. His works on the accurate value of pi describe the lengthy calculations involved. Zu used Liu Hui's π algorithm described earlier by Liu Hui to inscribe a 12,288-gon. Zu's value of pi is precise to six decimal places and for almost nine hundred years thereafter no subsequent mathematician computed a value this precise. Zu also worked on deducing the formula for the volume of a sphere with his son Zu Gengzhi. In their calculation, Zu used the concept that two solids with equal cross-sectional areas at equal heights must also have equal volumes to find the volume of a Steinmetz solid. And further multiplied the volume of the Steinmetz solid with π/4, therefore found the volume of a sphere as πd^3/6 (d is the diameter of the sphere).
In 488, Zu Chongzhi was responsible for erecting water powered trip hammer mills which was inspected by Emperor Wu of Southern Qi during the early 490s.