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Yang Hui __[]__ http://www.answers.com/topic/yang-hui Yang Hui, born in Chekiang province, wrote several different amazing mathematical text. The dates on his text showed that he may have lived towards the end of the Nan (Southern) Sung dynasty, but as a contemporary of both Oin Jiushao and Li Zhi, they showed work of fifteen years before Yangs work. Not much was written about him, but of Liu I who was a native of Chung-shan and taught mathematics to Yang as a child. Four of Yang’s friends were also interested in mathematics, but the only information about them are in Yang’s texts. Yang provided much proof for the proposition that the complements of the parallelograms, the same idea expressed in Euclid’s forty-third proposition of his first book. Yang’s writings show the first quadratic equations with negative coefficients of 'x' appear. Yang also had a well-known ability in manipulate decimal fractions. Yang expressed them in decimal parts.

Liu Yi

http://books.google.com/books?id=ACK1jreKgCoC&pg=PA142&lpg=PA142&dq=Liu+Yi+Mathematician&source=bl&ots=gdLHDJBAY0&sig=qtDWH-rRLEt0NeRlijwLSYhR4Uw&hl=en&ei=grYVStuqDsTVlQeLm4TLCw&sa=X&oi=book_result&ct=result&resnum=5#PPA137,M1 __[]__ Liu Yi lived in the Northern Song Dynasty as a mathematician. He was the first who annulled the restriction that the coefficients of an equation must be positive and the leading coefficient be 1. Liu Yi was said to have written a certain Yigu genyuan. Also he was known to have taught Yang Hui math as well. He developed the method of solving higher degree equations about 1019. It was called sanjustu. Liu Yi improved the method for root extraction to the Positive Negative Root Extraction algorithm. The method of estimating roots in this algorithm is very difficult, and mainly owing to this difficult problem, the theory of algebraic equations was far developed in the mid-Qing Dynasty.

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