Zu Chongzhi

To Chongzhi (Chinese祖 冲 之/祖 冲 之, Pinyin Zǔ Chongzhi, W.-G. TsuCh'ung -chih; * 429, † 500) was a Chinese mathematician and astronomer at the time of Liu Song and Southern Qi Dynasty.

Life and work

The ancestors of Chongzhi to come from the area of present-day Baoding ( Hebei ). Many Chinese came fleeing from the war in the area of the Eastern Jin Dynasty to the Yangtze River. With them came also to his grandfather Chang (祖 昌). This became the " Minister of Great Works " (大匠 卿) at the Liu Song, he was therefore responsible for the construction projects of the government. Zus father to Shuo (祖 朔) worked in court and was considered a respectable man.

He himself was born in Jiankang. As in his family long before it was a traditional tendency to astronomy and mathematics, his talent was up early and made ​​him known. As the Liu Song Xiaowu king learned of his talent, he sent him to the Academy of Hualin Xuesheng (华林 学 省) and later the Imperial University in Nanjing ( Zongmingguan ). In the year 461 he was the Governor in Nanxu (today Zhenjiang, Jiangsu).

Together with his son to Gengzhi published to Chongzhi a math book with the name " methods for interpolation ", which is one of the "Ten Mathematical Classics " ( Suanjing shi shu ). Although the book was lost during the time of the Song Dynasty, there are about its content but conjecture: for example, to the fact a number of astronomical calculations ( very precise because of that he designed calendar) as well as a formula for cubic equations, volume of the sphere and the circle constant π be included.

Astronomy

To was a gifted astronomer, of the periods could determine with great accuracy. His methods of interpolation and integration were far ahead of their time. It is said that even the astronomers of the Song Dynasty and the Indian astronomers influenced the Tang Dynasty found his methods confusing.

• The sidereal and tropical year: He recognized the wobbling of the earth and calculated 45 years and 11 months per degree, ie one revolution in 16530 years ( right: about 25,750 years = 71.5 years per degree ).
• Length of the year: He calculated the length of the year with 365.24281481 days (correctly: 365.24219878 days, ie 99.9998 % accurate ).
• Orbit of the moon: The circulation ratio of the Earth and Moon was determined with 27.21223 days (correctly: 27.21222 ). So that he could predict the four eclipses in the years 436-459. In the astrology - inspired Chinese an important date.
• Circulation of Jupiter: He calculated the orbital period of Jupiter with 11.858 years ( correct: 11.862 years ).
• The Daming calendar (大 明 历): Even as a student under He Chengtiansi he detected errors in the valid calendar system. Together with his teacher the Yuanjia calendar was designed to correct some errors in the old. To continue to work on the problem and found 463 Daming calendar before. However, the bureaucracy and the death of the emperor prevented his introduction to 510

Attention: If the astronomical sizes is important to note that average values ​​are used.

Mathematics

The mathematical work of to is described in his math book Zhui Shu. Most researchers argue about their complexity. Operated Traditionally Chinese mathematics with algebra and equations. It is therefore clear that the method described in the book. For used a polygon with 12,288 sides and calculated π so on eight -digit precision. It took 1000 years until someone was able to do likewise. He used the Cavalieri method ( about 1000 years before Bonaventura Cavalieri ), also a part of the integral calculus, in order to determine the volume of a sphere. He determined the spherical volume with R as the radius.

Determination of the circle number

He could calculate two values ​​of the wave number π. That was the best approximation for over 900 years. His best approximation was (密 率, Milu, " exact approximation " ) or 355/113, the second was (约 率, Yuelu, " rough approximation " ) or 22 / 7th He arrived at its result by using a 12,288 ( = 212 × 3) - sided polygon surrounding the circle.

The Japanese mathematician Yoshio Mikami explains:

" 22/7 has already been found by Archimedes centuries earlier. 355/113 but not found in any Indian, Arabic or Greek manuscript. The value was only found in 1585 by the Dutch mathematician Adriaan Anthoniszoon. These are nearly 1000 years after to Chongzhi. "

Yoshio Mikami therefore advocates to call the break as additions Chongzhi break. In Chinese literature it is known as At - Chongzhi ratio. It is the best rational description, until you come.

The Südweisende Cart

The Südweisende car was invented by the Chinese mechanic Ma Jun (ca. 200-265 ). It is to a car with an early version of the differential gear. This shows a figure on the car always to the south. It thus is pure mechanics and not a compass, which requires a magnetic field. The same technique is used in the car so as to transmit the same power to the wheels of an axle. At the end of the era of the three kingdoms of the car fell into oblivion. Nevertheless, we succeeded to Chongzhi of the car in the 478 rebuild. For this purpose in the book Song Shu (about 500) and After Chi Shu:

" When the Emperor of Liu Song Wi conquered the kingdom of Guanzhong, he captured the Südweisenden carriage of Yao Xing. But it was just a shell without the machine. A man had to rotate the figure inside. During the reign of Ming Sheng - commissioned " Gao Di " Zi Zu Chongzhi to reconstruct the car. He created a new machine made ​​of bronze which could rotate correctly and uniformly held that direction. Since Ma Jun has not been anything. "