我国古代的数学成就浅析
1万字 29页
摘要 数学科学具有悠久的历史，在世界数学的发展史上，中国古典数学发展到了高峰，取得了许多举世瞩目的成就。中国古典数学的形成、发展和兴盛经历了三次高峰：数学体系的形成——《周髀算经》与《九章算术》、数学稳步发展——刘徽与祖冲之的数学成就、数学发展的全盛时期——宋元数学成就。本文主要论述中国古代在数学方面的紷@龀删停趸铡案钤彩酢敝刑逑值奈⒎炙枷耄约按印毒耪滤闶酢贰胺匠淌酢钡较咝苑匠套槔砺鄣姆⒄埂Ⅻbr>关键词：数学成就 九章算术 刘徽 方程术
Just talk about the mathematics achievement of
ancient Chinese
Abstract Mathematics science has a long history , in the history of the development of the world of mathematics, the development of Chinese classical mathematics reached to its peak, and had made remarkable achievements. The formation ,development and prosperity of Chinese traditional mathematics has experienced three times of peak: the formation of a mathematical system -Zhou Bi Suan Jing and Jiu Zhang Suan Shu, the steady development of mathematics -the mathematics achievement of Liu Hui and Zu ChongZhi ,the heyday of mathematics development - the mathematics achievement of Song and Yuan dynasties. This paper mainly discusses the outstanding mathematics achievements made in ancient China, the differential ideas of Liu Hui’cyclotomic surgery, and the development of equation from the equation of the technique of Jiu Zhang Suan Shu to the theory of linear equations .
Key words:The mathematics achievement Jiu Zhang Suan Shu Liu Hui The equation of the technique
目 录
引言 …………………………………………………………………………………………… 1
第一章 中国古代主要的数学成就 …………………………………………………… 1
1.1 《周髀算经》……………………………………………………………………………1
1.2 《九章算术》……………………………………………………………………………2
1.3 祖冲之与祖暅的数学成就…………………………………………………………5
1.3.1 圆周率……………………………………………………………………………6
1.3.2 祖氏理论……………………………………………………………………………6
1.4 中国剩余定律………………………………………………………………………8
1.5内插法与垛积术…………………………………………………………………………9
1.6 天元术与四元术………………………………………………………………………11
1.6.1天元术 ……………………………………………………………………………11
1.6.2四元术 ……………………………………………………………………………12
第二章 从“割圆术”到微积分 ………………………………………………………… 14
2.1 刘徽的“割圆术” ……………………………………………………………………14
2.2 “割圆术”中的极限思想 ……………………………………………………………15
2.3 从“割圆术”到微积分………………………………………………………………15
第三章“方程术”与线性方程组理论…………………………………………………19
3.1《九章算术》“方程术”………………………………………………………………19
3.2线性方程组理论 ………………………………………………………………………20
结论……………………………………………………………………………………………26
致谢……………………………………………………………………………………………26
参考文献 ……………………………………………………………………………………26
