(429–500), courtesy name Wenyuan
(文遠), was a prominent Chinese
The term Chinese people may refer to any of the following:*People with Han Chinese ethnicity ....
during the Liu Song and Southern Qi
The Southern Qi Dynasty was the second of the Southern dynasties in China, followed by the Liang Dynasty. During its 23-year history, the dynasty was largely filled with instability, as after the death of the capable Emperor Gao and Emperor Wu, Emperor Wu's grandson Xiao Zhaoye was assassinated...
Life and works
Chongzhi's ancestry was from modern Baoding, Hebei
-Administrative divisions:Baoding prefecture-level city consists of 3 municipal districts, 4 county-level cities, 18 counties:-Demographics:The Baoding urban area has a population of around 1,006,000 . The population of the Baoding administrative area is 10,890,000. The considerable majority are...
. To flee from the ravage 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 "Minister of Great Works" ) within the Liu Song and was in charge of government construction projects. Zu's father, Zu Shuo (祖朔) also served the court and was greatly respected for his erudition.
Zu was born in Jiankang
Jiankang was the capital city of the Eastern Jin Dynasty and Southern Dynasties. Its walls are extant ruins in the modern municipal region of Nanjing.-History:...
. His family had historically been involved in astronomy 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
Emperor Xiaowu of Liu Song , personal name Liu Jun , courtesy name Xiulong , nickname Daomin , was an emperor of the Chinese dynasty Liu Song. He was a son of Emperor Wen. After his older brother Liu Shao assassinated their father in 453 and took the throne, he rose in rebellion and overthrew Liu...
heard of him, he was sent to an Academy, the Hualin Xuesheng (華林學省), and later at the Imperial Nanjing University (Zongmingguan) to perform research. In 461 in Nanxu (today Zhenjiang, Jiangsu
Zhenjiang is a prefecture-level city in the southwest of Jiangsu province in the eastern People's Republic of China . Sitting on the southern bank of the Yangtze River, it borders the provincial capital of Nanjing to the west, Changzhou to the east, and Yangzhou across the river to the north.Once...
), 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
(Method of Interpolation). There is a high possibility of astronomical calculation techniques due to the accuracy of his calendars. It is said that the treatise contains formulas for the volume of the sphere, cubic equations and the accurate value of pi. Sadly, this book didn't survive to the present day, since it has been lost since the Song Dynasty
The Song Dynasty was a ruling dynasty in China between 960 and 1279; it succeeded the Five Dynasties and Ten Kingdoms Period, and was followed by the Yuan Dynasty. It was the first government in world history to issue banknotes or paper money, and the first Chinese government to establish a...
His mathematical achievements included:
- the Daming calendar (大明曆) 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 very close to 365.24219878 days as we know today.
- calculating the number of overlaps between sun and moon as 27.21223, which is very close to 27.21222 as we know today; using this number he successfully predicted an eclipse four times during 23 years (from 436 to 459).
- calculating the Jupiter year as about 11.858 Earth years, which is very close to 11.862 as we know of today.
- deriving two approximations of pi
' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...
, 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 (密率, Milü, detailed approximation) and 22⁄7 (約率, Yuelü, rough approximation) being the other notable approximations. He obtained the result by approximating a circle with a 12,288 (= 212 × 3) sided polygon. This was an impressive feat for the time, especially considering that the device Counting rods
Counting rods are small bars, typically 3–14 cm long, used by mathematicians for calculation in China, Japan, Korea, and Vietnam. They are placed either horizontally or vertically to represent any number and any fraction....
he used for recording intermediate results were merely a pile of wooden sticks laid out in certain patterns. Japanese mathematician Yoshio Mikami
was a Japanese mathematician and wasan historian. He was born February 16, 1875 in Kotachi, Hiroshima prefecture. He attended the High School of Tohoku University, and in 1911 was admitted to Imperial University of Tokyo. He studied history of Japanese and Chinese mathematics. In 1913, he...
pointed out, " was nothing more than the π value obtained several hundred years earlier by the Greek mathematician Archimedes
Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an...
, however Milu could not be found in any Greek, Indian or Arabian manuscripts, not until 1585 Dutch
The Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...
mathematician Adriaan Anthoniszoom obtained this fraction; the Chinese possessed this most extraordinary fraction over a whole millennium earlier than Europe". Hence Mikami strongly urged that the fraction be named after Zu Chongzhi as Zu Chongzhi fraction. In Chinese literature, this fraction is known as "Zu rate". Zu rate 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 (equivalent to 4πr3/3).
Zu was an accomplished astronomer who calculated the values of time with unprecedented precision. His methods of interpolating and the usage of integration is far ahead of his time. Even the astronomer Yi Xing
Yi Xing , born Zhang Sui , was a Chinese astronomer, mathematician, mechanical engineer,and Buddhist monk of the Tang Dynasty...
's isn't comparable to his value (who was beginning to utilize foreign knowledge). 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 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 scholars 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 the method of exhaustion
The method of exhaustion is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape. If the sequence is correctly constructed, the difference in area between the n-th polygon and the containing shape will...
discovered and described 700 years earlier by Archimedes to inscribe a 12,288-gon. Zu's value of pi is precise to six decimal places and for a thousand years thereafter no subsequent mathematician computed a value this precise. Zu also worked on deducing the formula for the volume of a sphere.
The South Pointing Chariot
The South Pointing Chariot
The south-pointing chariot was an ancient Chinese two-wheeled vehicle that carried a movable pointer to indicate the south, no matter how the chariot turned. Usually, the pointer took the form of a doll or figure with an outstretched arm...
device was first invented by the Chinese mechanical engineer Ma Jun
Ma Jun , style name Deheng , was a Chinese mechanical engineer and government official during the Three Kingdoms era of China...
(c. 200-265 AD). It was a wheeled vehicle that incorporated an early use of differential gears to operate a fixed figurine that would constantly point south, hence enabling one to accurately measure their directional bearings. This effect was achieved not by magnetics (like in a compass
A compass is a navigational instrument that shows directions in a frame of reference that is stationary relative to the surface of the earth. The frame of reference defines the four cardinal directions – north, south, east, and west. Intermediate directions are also defined...
), but through intricate mechanics, the same design that allows equal amounts of torque applied to wheels rotating at different speeds for the modern automobile
An automobile, autocar, motor car or car is a wheeled motor vehicle used for transporting passengers, which also carries its own engine or motor...
. After the Three Kingdoms
The Three Kingdoms period was a period in Chinese history, part of an era of disunity called the "Six Dynasties" following immediately the loss of de facto power of the Han Dynasty rulers. In a strict academic sense it refers to the period between the foundation of the state of Wei in 220 and the...
period, the device fell out of use temporarily. However, it was Zu Chongzhi who successfully re-invented it in 478 AD, as described in the texts of the Song Shu
(c. 500 AD) and the Nan Chi Shu
, with a passage from the latter below:
When Emperor Wu of Liu Song
Emperor Wu of Song , personal name Liu Yu , courtesy name Dexing , nickname Jinu , was the founding emperor of the Chinese dynasty Liu Song. He came from a humble background, but became prominent after leading a rebellion in 404 to overthrow Huan Xuan, who had usurped the Jin throne in 403...
Guanzhong , or Guanzhong Plain, is a historical region of China corresponding to the lower valley of the Wei River. It is called Guanzhong or 'within the passes' to distinguish it from 'Guandong' or 'east of the pass', that is, the North China Plain. The North China Plain is bordered on the west by...
he obtained the south-pointing carriage of Yao Xing, but it was only the shell with no machinery inside. Whenever it moved it had to have a man inside to turn (the figure). In the Sheng-Ming reign period, Gao Di commissioned Zi Zu Chongzhi to reconstruct it according to the ancient rules. He accordingly made new machinery of bronze, which would turn round about without a hitch and indicate the direction with uniformity. Since Ma Jun's time such a thing had not been.
Named for him
- as Zu Chongzhi rate.
- The lunar crater Tsu Chung-Chi
Tsu Chung-Chi is a relatively small lunar impact crater on the Moon's far side. It lies to the west-southwest of the crater Leonov, and to the northeast of the large walled plain Mendeleev. To the north of Tsu Chung-Chi is the Mare Moscoviense, one of the few maria on the Moon's far side.This is a...
- 1888 Zu Chong-Zhi
1888 Zu Chong-Zhi is a main-belt asteroid discovered on November 9, 1964 by Purple Mountain Observatory at Nanking.- External links :*...
is the name of asteroid
Asteroids are a class of small Solar System bodies in orbit around the Sun. They have also been called planetoids, especially the larger ones...
- Needham, Joseph (1986). Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth. Cambridge University Press