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Zhao Shuang, also known as baby, Zi Junqing. Three Kingdoms Wu people, one said Wei, or Han Chinese. Origin, date of birth unknown. Mathematics, astronomers.
Zhao Shuang claims paid more than negative days of "Zhou Bi", therefore abandoned the for injection, showing a non-mathematicians from the days of manual labor. Is generally believed that, "Zhou Bi Suan Jing," was written in around 100 BC, is a reference to scores of computing and the Pythagorean theorem and other mathematical methods described celestial dome of astronomy books. And about the same time a book of "String" made it clear that the Pythagorean theorem and some of the solutions of Gougu Xing problem. Zhao Shuang, "Zhou Bi Suan Jing Note" paragraph by paragraph to explain "Zhou Bi" scriptures. The most exciting is the appendix in the first chapter of the Pythagorean circle square, a short 500 word summary of "Zhou Bi Suan Jing", "String" "String" the Chinese people since the success of Pythagorean arithmetic , which contains the Pythagorean theorem Pythagorean theorem (here to a, b, c represent the hook right triangle, stocks, triangular chord length) a ^ 2 + b ^ 2 = C ^ 2 and the deformation of b ^ 2 = c ^ 2-a ^ 2 = (ca) (c + a), a ^ 2 = c ^ 2-b ^ 2 = (cb) (c + b), c ^ 2 = 2ab + (ba) ^ 2; have passed from the square opening with a ^ 2 + (ba) a = 1 / 2 [c ^ 2 - (ba) ^ 2] seek hook a, open square a = [c ^ 2 - (c ^ 2-a ^ 2 )] ^ 1 / 2 request hook a, open with from the square (ca) ^ 2 +2 a (ca) = c ^ 2-a ^ 2 ca seeking hook string difference method, and c = (ca) + a, c + a = b ^ 2 / (c-1), ca = b ^ 2 / (c + a), c = [(c = a) ^ 2 + b ^ 2] / 2 (c + a), a = [(c + a) ^ 2-b ^ 2] / 2 (c + a) and other formulas, with the above formula symmetry, but also seek b, cb, c + b and the cb, c + b demand c, b the formula , another difference from the hook string, the stock strings hook poor demand, shares of the string formula a = [2 (ca) (cb)] ^ 1 / 2 + (cb), b = [2 (ca) (cb)] ^ 1 / 2 + (ca), c = [(2 (ca) (cb)] ^ 1 / 2 + (cb) + (ca) and the Pythagorean difference b-a and the Pythagorean and b + a relation (a + b ) ^ 2 = 2c ^ 2 - (ba) ^ 2, a + b = [2c ^ 2 - (ba) ^ 2] ^ 1 / 2, ba = [2c ^ 2 - (b + a) ^ 2] ^ 1 / 2, then this gives the request a, b of the formula b = 1 / 2 [(a + b) + (ba)], a = 1 / 2 [(a + b) - (ba)], Finally, from the string and hook (or shares) that the shares (or hook) and with the stock strings (or hook) the difference between String difference:
(C + b) - (cb) = [(2c) ^ 2-4a ^ 2] ^ 1 / 2
(C + a) - (ca) = [(2c) ^ 2-4b ^ 2] ^ 1 / 2
Zhao Shuang complementarity with the access method were to prove the above formula. Most of these formulas and the "String" and Liu Hui set forth in the same note, that method is similar, but note the last two formulas are not as Liu Hui, and Liu Hui also used slightly different terminology. Shows that this knowledge is the consensus of mathematicians Han period. "Domain Biographies," said Pythagorean Elements Legend "Five hundred words ear, then several thousand people who can not detail, are Gold Vase exhaustive, intensive nutshell, the most honest operator's it."
Literature
Original literature
[1] (NG) Zhao Shuang Note: The Zhou Bi Suan Jing, see Qian Bao Cong school point "Ten Classics" Book, Zhonghua, 1963.
Literature
[2] Qian Bao-cong Editor: History of Chinese Mathematics, Science Press, 1964.
[3] Qian Bao-cong: Zhou Bi Suan Jing test, see the "money Baocong selected articles from the history of science", Science Press, 1983.
[4] (clear) Ruan editor: domain human transmission, the Commercial Press reprint, 1955.
(Science Press, "Ancient Chinese scientists biography")
Zhao Shuang, Soochow mathematician Three Kingdoms period. Who note, "Zhou Bi Suan Jing," he's "Zhou Bi Suan Jing note" in a "Pythagorean Elements Legend" Five hundred word text, together with cloud illustrations (already lost), the text of this note succinctly summed up the importance of the Eastern Han Dynasty Pythagorean arithmetic results, first presented and proved the Pythagorean triangular string and and, and poor relations more than 20 propositions that he is mainly based on geometric area of the conversion relationships .
Zhao Shuang was still "Pythagorean Elements Legend" Roots derive quadratic equations and formulas in the "high chart note on" area of the use of geometric relations, given the weight difference technique of proof. (Han astronomers measure the sun high and far is called a weight difference technique).
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