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

Abstract

In this paper, we deal with recent researches on Ying Nu(Ying Nu ) and
Ying Buzu(Ying Zu ) which were addressed in the book Jiu Zhang Suan Shu(Zhang Suan Shu ,
The Nine Chapters on the Mathematical Art). Ying Nu(Ying Buzu) is a concept on
profit and loss problems. Ying Buzu Shu(Ying Zu Shu , 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
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'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 Nu(Ying Buzu) in the
book Suan Xue Bao Jian(Suan Xue Bao Jian ).