项名达递加图与牛顿二项式定理

Xiang Mingda's Binomial Array and Newton's Binomial Theorem

本文详细分析了清代数学家项名达构造递加图的过程和“以根求积法”的来由,从而说明项名达独立于牛顿实质上给出了(1+x)^(n/m)(n/m为任意正负有理数)形式的二项式定理的系数表及计算公式。

The paper discusses in detail the process of making DIJATU ( Binomial Array ) by Xi’ang Ming-Da, a mathematician in Qing Dynasty ( 1789-1850 ) , and the source of YIGENQIUJIFA. It shows that Xiang had essentially worked out the binomial array and it’s calculation formule in the form ofis any rational number) which was independent of Newton’s model.