Wang Xiaotong
Encyclopedia
Wang Xiaotong (AD 580
–640
), also known as Wang Hs'iao-t'ung, was a Chinese mathematician and calendarist. He is famous as the author of the Jigu Suanjing
(Continuation of Ancient Mathematics) one of the Ten Computational Canons.
He presented this work to Li Yuan the first emperor of the Tang dynasty
, along with a brief biography.
According to this autobiography, he became interested in mathematics at a young age. After a study of the Nine Chapters on the Mathematical Art and particularly Liu Hui
's commentary on it, Wang became a teacher of mathematics, and later deputy director of the Astronomical Bureau.
It was known that the Chinese calendar
at that time was in need of reform since, although only in operation for a few years, already predictions of eclipse
s were getting out of step. In 623, together with Zu Xiaosun
, a Civil Servant, he was assigned to report on problems with the calendar—although only recently adopted, it was already out of step with the eclipses. In fact Wang did not approach this is a sophisticated way; he proposed to ignore the irregularity of the sun's motion and also the precession of the equinox
es -- both had already been incorporated in calendar calculations by Zu Chongzhi
in the fifth century.
s; it was included as one of the Ten Computational Canons when reprinted in 1084.
The book contains 20 problems based mostly on engineering construction of astronomic observation tower, dike, excavation of a canal bed etc. and right angled triangles, but which in essence deal with the solution of cubic equations, the first known Chinese work to deal with them.
In Jigu Suanjin, Wang established and solved 25 cubic equations of the form:
, along with 2 quadratic equation
s and 2 double quadratic equation
s.
Wang's work influence later Chinese mathematicians, but it is said that it was his ideas on cubic equations which influenced Fibonacci
after transmission via the Islamic world.
580
Year 580 was a leap year starting on Monday of the Julian calendar. The denomination 580 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.- Europe :* Ethelbert becomes king of Kent.* The Roman...
–640
640
Year 640 was a leap year starting on Saturday of the Julian calendar. The denomination 640 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.- Europe :* Tulga succeeds his father Suinthila as king...
), also known as Wang Hs'iao-t'ung, was a Chinese mathematician and calendarist. He is famous as the author of the Jigu Suanjing
Jigu Suanjing
Jigu suanjing was the work of early Tang dynasty calendarist and mathematician Wang Xiaotong, written some time before the year 626, when he presented his work to the Emperor...
(Continuation of Ancient Mathematics) one of the Ten Computational Canons.
He presented this work to Li Yuan the first emperor of the Tang dynasty
Tang Dynasty
The Tang Dynasty was an imperial dynasty of China preceded by the Sui Dynasty and followed by the Five Dynasties and Ten Kingdoms Period. It was founded by the Li family, who seized power during the decline and collapse of the Sui Empire...
, along with a brief biography.
According to this autobiography, he became interested in mathematics at a young age. After a study of the Nine Chapters on the Mathematical Art and particularly Liu Hui
Liu Hui
Liu Hui was a mathematician of 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 mathematic known as The Nine Chapters on the Mathematical Art .He was a...
's commentary on it, Wang became a teacher of mathematics, and later deputy director of the Astronomical Bureau.
It was known that the Chinese calendar
Chinese calendar
The Chinese calendar is a lunisolar calendar, incorporating elements of a lunar calendar with those of a solar calendar. It is not exclusive to China, but followed by many other Asian cultures as well...
at that time was in need of reform since, although only in operation for a few years, already predictions of eclipse
Eclipse
An eclipse is an astronomical event that occurs when an astronomical object is temporarily obscured, either by passing into the shadow of another body or by having another body pass between it and the viewer...
s were getting out of step. In 623, together with Zu Xiaosun
Zu Xiaosun
Zu Xiaosun was a Chinese temperament expert of Sui and Tang period. During the Kaihuang period he was appointed as Xielülang , joined the melodizing of ritual music, and received orders to learn the Jingfang Temperament from Mao Shuang...
, a Civil Servant, he was assigned to report on problems with the calendar—although only recently adopted, it was already out of step with the eclipses. In fact Wang did not approach this is a sophisticated way; he proposed to ignore the irregularity of the sun's motion and also the precession of the equinox
Equinox
An equinox occurs twice a year, when the tilt of the Earth's axis is inclined neither away from nor towards the Sun, the center of the Sun being in the same plane as the Earth's equator...
es -- both had already been incorporated in calendar calculations by Zu Chongzhi
Zu Chongzhi
Zu Chongzhi , courtesy name Wenyuan , was a prominent Chinese mathematician and astronomer during the Liu Song and Southern Qi Dynasties.-Life and works:...
in the fifth century.
Jigu Suanjing
His major contribution was the Jigu suanjing ("Continuation of Ancient Mathematics" 缉古算经), written before year 626. Jigu Suanjing became a text for the Imperial examinationImperial examination
The Imperial examination was an examination system in Imperial China designed to select the best administrative officials for the state's bureaucracy. This system had a huge influence on both society and culture in Imperial China and was directly responsible for the creation of a class of...
s; it was included as one of the Ten Computational Canons when reprinted in 1084.
The book contains 20 problems based mostly on engineering construction of astronomic observation tower, dike, excavation of a canal bed etc. and right angled triangles, but which in essence deal with the solution of cubic equations, the first known Chinese work to deal with them.
In Jigu Suanjin, Wang established and solved 25 cubic equations of the form:
, along with 2 quadratic equationQuadratic equation
In mathematics, a quadratic equation is a univariate polynomial equation of the second degree. A general quadratic equation can be written in the formax^2+bx+c=0,\,...
s and 2 double quadratic equation
Quadratic equation
In mathematics, a quadratic equation is a univariate polynomial equation of the second degree. A general quadratic equation can be written in the formax^2+bx+c=0,\,...
s.
Wang's work influence later Chinese mathematicians, but it is said that it was his ideas on cubic equations which influenced Fibonacci
Fibonacci
Leonardo Pisano Bigollo also known as Leonardo of Pisa, Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci, or, most commonly, simply Fibonacci, was an Italian mathematician, considered by some "the most talented western mathematician of the Middle Ages."Fibonacci is best known to the modern...
after transmission via the Islamic world.
Sources
- J-C Martzloff, A history of Chinese mathematics (Berlin-Heidelberg, 1997).
- J-C Martzloff, Histoire des mathématiques chinoises (Paris, 1987).
- Y Mikami, The Development of Mathematics in China and Japan, chapter 8 Wang Hsiao-Tung and Cubic Equations, pp 53–56, reprint of 1913 ed (New York, 1974).
- B Qian (ed.), Ten Mathematical Classics (Chinese) (Beijing, 1963).
- Y Ruan, Biographies of Mathematicians and Astronomers (Chinese) 1 (Shanghai, 1955).
- K Shen, J N Crossley and A W-C Lun, The nine chapters on the mathematical art : Companion and commentary (Beijing, 1999).