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http://dx.doi.org/10.11568/kjm.2012.20.1.137

AN ANALYSIS OF RECENT RESEARCH ON THE METHOD OF EXCESS AND DEFICIT (Ying NÜ and Ying Buzu Shu)  

Lee, Sang-Gu (Department of Mathematics, Sungkyunkwan University)
Lee, Jae Hwa (BK21 Math. Modeling HRD Div., Sungkyunkwan University)
Publication Information
Korean Journal of Mathematics / v.20, no.1, 2012 , pp. 137-159 More about this Journal
Abstract
In this paper, we deal with recent researches on Ying N$\ddot{u}$ and Ying Buzu(盈不足) which were addressed in the book Jiu Zhang Suan Shu(九章算術, The Nine Chapters on the Mathematical Art). Ying N$\ddot{u}$(Ying Buzu) is a concept on profit and loss problems. Ying Buzu Shu(盈不足術, the method of excess and deficit) represents an algorithm which has been used for solving many mathematical problems. It is known as a rule of double false position in the West. We show the importance of Ying Buzu Shu via an analysis of some problems in 'Ying Buzu' chapter. In 1202, Fibonacci(c.1170-c.1250) used Ying Buzu Shu in his book. This shows some of Asian mathematics were introduced to the West even before the year 1200. We present the origin of Ying Buzu Shu, and its relationship with Cramer's Rule. We have discovered how Asia's Ying Buzu Shu spread to Europe via Arab countries. In addition, we analyze some characters of Ying N$\ddot{u}$(Ying Buzu) in the book Suan Xue Bao Jian(算學寶鑑).
Keywords
Ying N$\ddot{u}$; Ying Buzu (Shu); Jiu Zhang Suan Shu; The Nine Chapters on the Mathematical Art; Suan Shu Shu(算數書); Suan Xue Bao Jian(算學寶鑑); Fibonacci;
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