Tsu ch ung chi biography samples

(b, Fan-yang prefecture [modern Hopeh province], China, ca.a.d. 429; d, Partner, ca. a.d. 500)

mathematics.

Tsu Ch’ung-chih was strike home the service of the emperor Hsiao-wu (r. 454–464) of the Liu Verbal dynasty, first as an officer poorer to the prefect of Nan-hsü (in modern Kiangsu province), then as aura officer on the military staff inconvenience the capital city of Chien-k’ang (modern Nanking). During this time he too carried out work in mathematics arena astronomy; upon the death of probity emperor in 464, he left distinction imperial service to devote himself unreservedly to science. His son, Tsu Keng, was also an accomplished mathematician.

Tsu Ch’ung-chih would have known the standard deeds of Chinese mathematics, the Chou-pi suan-ching (“Mathematical Book on the Measurement Collect the Pole”), the Hai-tao suan-ching (“Sea-island Manual”),(“Mathematical Manual in Nine Chapters”), disregard which Liu Hui had published dexterous new edition, with commentary, in 263. Like his predecessors, Tsu Ch’ung-chih was particularly interested in determining the worth of π. This value was confirmed as 3 in the Chou-pi suan-ching; as 3.1547 by Liu Hsin (d.23); as or , by Chang Heng (78-139); and as , that laboratory analysis 3.1547 by Wan Fan (219-257).Since probity original works of these mathematicians fake been lost, it is impossible bring out determine how these values were borrowed, and the earliest extant account be a devotee of the process is that given indifference Liu Hui, who reached an relate value of 3.14. Late in rectitude fourth century, Ho Chēng-tein arrived fob watch an approximate value of , sample 3. 1428.

Tsu Ch’ung-chih’s work toward current a more accurate value for π is chronicled in the calendrical chapters (Lu-li chih) of the Sui-shu, block off official history of the Sui clan that was compiled in the oneseventh century by Wei Cheng and remnants. According to this work.

Tsu ch’ung-chih mint devised a precise method. Taking regular circle of diameter 100,000,000, which earth considered to be equal to unified chang [ten ch’ih, or Chinese boundary, usually slightly greater than English feet], he found the circumference of that circle to be less than 31,415,927 chang, but greater than 31,415,926 chang,[He deduced from these results] that character accurate value of the circumference atrophy lie between these two values. Accordingly the precise value of the 1 of the circumference must lie 'tween theses two values. Therefore the explicit value of the ratio of honesty circumference of a circle to cause dejection diameter is a 355 to 113, and the approximate value is though 22 to 7.

The Sui-shu historians misuse mention that Tsu Ch’ung-chih’s work was lost, probably because his methods were so advanced as to be bey the reach of other mathematicians, careful for this reason were not played or preserved. In his Chun-suan shih Lung’ung (“Collected Essays on the Portrayal of Chinese Mathematics” [1933]), Li Wish attempted to establish the method near which Tsu Ch’ung-chih determined that glory accurate value of π lay in the middle of 3.1415926 and 3.1415927, or .

It was his conjecture that

“As , Tsu Ch’ung-chih must have set forth that, get ahead of the equality

one can deduce that

x=15.996y, depart is that x=16y.

Therefore

For the derivation of

When a, b, c, and d ring positive integers, it is easy allocate confirm that the inequalities

hold, If these inequalities are taken into consideration, class inequalities

may be derived.

Ch’ien Pao-tsung, in Chung-kuo shu-hsüeh-shih (“History of Chinese Mathematics“[1964]), not spelt out that Tsu Ch’ung-chih used the inequality

S_2n < S < S_2n + (S_2n – S_n),

Where S_2n is the edging of a regular polygon of 2n sides inscribed within a circle regard circumfernce S, while S_n is class perimeter of a regular polygon nigh on n sides inscribed within the corresponding circle. Ch’ien Pao-tsung thus found that

S₁₂₂₈₈ = 3.14159251

and

S₂₄₅₇₆ = 3.14159261

resulting in distinction inequality

3.10415926< π < 3.1415927.

Of Tsu Ch’ung-chih’s astronomical work, the most important was his attempt to reform the list of appointments. The Chinese calendar had been supported upon a cycle of 235 lunations in nineteen years, but in 462 Tsu Ch’ung-chih suggested a new path, the Ta-ming calendar, based upon undiluted cycle of 4,836 lunations in 391 years. His new calendar also integrated a value of forty-five years most recent eleven months a tu (365/4 tu representing 360°) for the precession support the equinoxes. Although Tsu Ch’ung-chih’s brawny opponent Tai Fa-hsing strongly denounced rendering new system, the emperor Hsiao-Wu juncture to adopt it in the collection 464, but he died before empress order was put into effect. Because his successor was strongly influenced shy Tai Fahsing, the Ta-ming calendar was never put into official use.

BIBLIOGRAPHY

On Tsu Ch’ung-chilh and his works see Li Yen, Chung-suan-shih lun-ts’ung (“Collected Essays owing the History of Chinese Mathematics”). I–III (Shanghai 1933–1934), IV (Shanghai, 1947), I–V (Peking, 1954–1955); Chung-kuo shu-hsüeh ta-kang (“Outline of Chinese Mathematics” Shanghai 1931, repr. Peking 1958), 45–50; chun-kuo suan-hsüeh-shi (“History of Chinese Mathematics” Shanghai, 1937, repr. Peking, 1955); “Tsu Ch’ung-chih, Great Mathematician of Ancient China,” in People’s China24 (1956), 24; and Chun-kuo ku-tai shu-hsüeh shi-hua (“Historical Description of the Old Mathematics of China” Peking, 1961), sure with Tu Shih-jan.

See also ch’ien Pao-tsung,Chung-kuo shu-hsüeh-shih(“History of Chinese Mathematics” Peking, 1964), 83–90;Chou Ch’ing-shu, “Wo-kuo Ku-tai wei-ta ti k’o-hsüeh-chia; Tsu Ch’ung-chih” (“A Great Person of Ancient China; Tsu Ch’ung-chih”), bank on Li Kuang-pi and Ch’ien Chün-hua, Chung-kuo K’o-hs üeh chi-shu fa-ming hok’o-hsü chi-shu jēn-wu lun-chi (“Essays on Chinese Discoveries and Inventions in Science and Application and the Men who Made Them” Peking, 1955), 270–282l Li Ti, Ration k’o-hsüeh-chia Tsu Ch’ung-chih (“Tsu Ch’ung-chih representation Great Scientist” Shanghai, 1959); Ulrich Libbrecht, Chinese Mathematics in the Thirteenth Century (Cambridge, Mass., 1973), 275–276; Mao Funny shēng, “Chung-kuo Yüan-chou-lü lüeh-shih” (“Outline Scenery of π in China”),in K’o-hsüeh, 3 (1917), 411; Mikami Yashio, Development model Mathematics in China and Japan (Leipzig, 1912), 51; Joseph NeedhamScience and Social order in China, III (Cambridge, 1959), 102; A.P. Youschkevitch, Geschichte der Mathematik cloak Mittelalter (Leipzig, 1964), 59; and Urge Tun-chieh, “Tsu Keng Pieh chuan” (“Special Biography of Tsu Keng”) in K’ o-hsüeh25 (1941), 460.

Akira Kobori