A Research On The History Of The Method To The Hundred Fowls Problem

The hundred fowls problem, which firstly appeared in Zhang Qiujian suanjing张丘建算经(Zhang Qiujian's Mathematical Treatise)approximately brought out in 5th century, played a tremendously important role in history of Traditional Chinese mathematics and mathematics-transmission. Based on predecessors'studies, this paper chose the method to the hundred fowls problem as disquisitive object, depending on thematic analysis of Suanxue baojian算学宝鉴(Precious Mirror of Mathematics, 1524)composed by Wang Wensu, Tongwen suanzhi同文算指(Mathematical Manual of Transmission,1614)compiled by Li Zhizao and Matteo Ricci, Suanhai shuoxiang算海说详( A Detailed Manual Of Mathematical Ocean,1659)composed by Li Changmao and Liber Abbaci(计算之书,1202)composed by Leonardo Fibonaci to afresh construct its evolvement and discusses the transmission of the hundred fowls problem between China and the West.Wang Wensu spent thirty years to accomplish Suanxue baojian, which has forty-one chapters. He collected the arithmetic of Yang Hui, Du Wengao, Xia Zeyuan and Jin Laipeng to be compiled, amend and innovate. In the twenty-seventh chapter of this book, which was namd Zhonglv fenshen众率分身, the hundred fowls problem was discussed. This paper indicated that based on the method of Biangu tongyuan辩古通源(A Debate And Source About Ancient Mathematics), Wang Wensu skillfully established Fangcheng方程and transformed fraction into integer by intricate numbers错综之数, giving the rate of increase and decrease and a feasible testing method to the hundred fowls problem. Moreover, through flexibly utilizing two different testing methods, He could solve problem which had more than ten unknowns. Therefore, Wang Wensu broke through the restrict of the hundred fowls problem before, discussing the problem finely, deeply and unprecedentedly and boosting the method to the problem successfully. The method of Suanxue baojian was the peak on the history of the method to the hundred fowls problem and had a vital status to its historical division.Tongwen suanzhi was a try to integrate Western mathematics with Traditional Chinse mathematics. In its third chapter, there was a vagarious method which was called the method of Hejiao sanlv和较三率to the hundred fowls problem. The core thought of it was to gain the rate of each unknown by the difference among the price, and then solve the problem. This was a almost almighty method, the connotation of which was different from the traditional method, because the integral answer was not demanded. This paper trended to argue that the method differed from not only the method of Western mathematics but also the method of Traditional Chinse mathematics, and that it was mixed-blood. Tongwen suanzhi had an important meaning for rebuilding the transmission of the hundred fowls problem between China and the West.Liber Abbaci had the thirty birds problem which was similar to the hundred fowls problem and Leonardo Fibonaci's solution was the method of alloys. It was a particular method to the diophantine equation, the core idea of which was accord with the method of Tongwen suanzhi. Although it was a testing method, it was still feasible when the numbers were small. This peaer's analyse was not only helpful to compare the difference between Western mathematics and Traditional Chinse mathematics in a same mathematic problem, but also had a positive meaning for proving up whether the method of alloys was the source of the method of Tongwen suanzhi.In Suanhai shuoxiang, there was a bizarre method which was called the method of Guijian xianghe chafen贵贱三位相和差分to the hundred fowls problem. Besided the problem and the idiographic testing process, the method was almost as the same as the method of alloys. This method covered with Traditional Chinse mathematics while its heart was Western mathematics. The significance of it made chear both the diversity of Chinse mathematics and the transmission of the hundred fowls problem between China and the West. On the hundred fowls problem, the methods of Liber Abbaci, Tongwen suanzhi and Suanhai shuoxiang came down in one continuous line, so the transmission of the hundred fowls problem between China and the West probably existed as to look Tongwen suanzhi as a agency. The gradual progress was not shaped as making copies by writing but the configuration of method changed in every term. The historical fact that the configuration of Li Changmao's method extremely resembled the one of Leonardo Fibonaci's methods represented the internal logic of mathematics.Based on the research above, this paper afresh constructed the evolvement of the method to the hundred fowls problem. And it indicated that there existed a predominant approach and several subordinate approachs forming the history in traditional epoch of the problem. The predominant approach, whose name was the method of Sanse Chafen三色差分and whose main idea was to reduce the amount of unknowns, progressed from Yanghui to Chen Dawei and culminated at Shi Yuechun. The subordinate approachs consisting of the method of Leonardo Fibonaci, Wang Wensu, Li Changmao and Tongwen suanzhi were anfractuous and difficult to be identified. All above built up the intricate historical evolvement of the method to the hundred fowls problem.This paper argued that the theoretical root of the method to the hundred fowls problem was different from the modern mathematics. Its historical process was a result of the effects of the mechanised character and the supposing method of Traditional Chinse mathematics. Therefore, the method of Sanse Chafen which accorded best with the two qualifications, dominated the history of the method to the hundred fowls problem. Furthermore, the funny methods of Wang Wensu and Li Changmao also enriched the history while the method of Tongwen Suanzhi glittered in the background of the transmission between Western mathematics with Traditional Chinse mathematics.It might be a regret that the main idea of the method to the hundred fowls problem in Zhang Qiujian suanjing was vague. But also due to it, so brilliant and fascinating the historical evolvement of the method to the hundred fowls problem was. A mathematical problem finally came into being a gorgeous chapter in the history of mathematics, and then it was no doubt to do this research for the positive significance.