| 穷竭法的历史及有关问题初探 |
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| 引用本文： | 邵明湖.穷竭法的历史及有关问题初探[J].辽宁师范大学学报(自然科学版),1990(1). |
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| 作者姓名： | 邵明湖 |
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| 作者单位： | 辽宁师范大学数学系 |
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| 摘 要： | 研究了穷竭法的历史,探讨了它与极限、积分等概念的关系,认为穷竭法是一种基于潜无穷观的严格的数学证明方法,是柯西极限理论的真正肇始;它可以视为一种极简单的积分,其思想早已渗透到了分析学中。
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| 关 键 词： | 穷竭法 无穷 极限 积分 |
The History of the Method of Exhaustion and Related Problems |
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| Shao Minghu.The History of the Method of Exhaustion and Related Problems[J].Journal of Liaoning Normal University(Natural Science Edition),1990(1). |
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| Authors: | Shao Minghu |
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| Institution: | Shao Minghu Department of Mathematics,Liaoning Normal University |
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| Abstract: | The method of exhaustion is an important method in the history of ancient
mathematics.Its emergence and development reflect the mathematicians' ideas on
some mathematical concepts such as infinite,limit,integral,etc.This paper studies
the history of the method and discusses its relations to limit,integral,etc.
The conclusions are that the method of exhaustion is rigorous proving method
based on the potential infinite view,and that it is the very beginning of Gauchy's
theory of limit.It can be viewed as one kind of simple integral,and its spirit
has permeated through the calculus. |
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| Keywords: | the method of exhaustion infinite limit integral |
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