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The Unique Achievement of 《SanHak JeongEui 算學正義》on KaiFangFa with count-wood: The refinement of ZengChengKaiFangFa through improvement of estimate-value array

산대셈 개방법(開方法)에 대한 《산학정의》의 독자적 성취: 어림수[상(商)] 배열법 개선을 통한 증승개방법(增乘開方法)의 정련(精鍊)

  • Received : 2018.08.20
  • Accepted : 2018.12.12
  • Published : 2018.12.31

Abstract

The KaiFangFa開方法 of traditional mathematics was completed in ${\ll}$JiuZhang SuanShu九章算術${\gg}$ originally, and further organized in Song宋 $Yu{\acute{a}}n$元 dinasities. The former is the ShiSuoKaiFangFa釋鎖開方法 using the coefficients of the polynomial expansion, and the latter is the ZengChengKaiFangFa增乘開方法 obtaining the solution only by some mechanical numerical manipulations. ${\ll}$SanHak JeongEui算學正義${\gg}$ basically used the latter and improved the estimate-value array by referring to the written-calculation in ${\ll}$ShuLi JingYun數理精蘊${\gg}$. As a result, ZengChengKaiFangFa was more refined so that the KaiFangFa algorithm is more consistent.

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