刘徽关于无理数的论述

Liu Hui's Exposition on Irrational Numbers

以往的中算史论著,总认为中国古代传统数学没有涉及无理数的讨论,其实这是一种误解。本文阐明从公元263年刘徽的《九章算术注》发现:早在刘徽之前,中算家不仅有了无尽方根的概念,而且掌握和运用了根式的一些基本运算性质。这是一个十分令人惊异的史实!

In most of the works on the history of Chinese Mathematics, it is generally believed that the ancient Chinese traditional mathematics never produced any thesis concerning irrational numbers, but, as a matter of fact, this idea proves to be a misunderstanding. Some years ago, in read- ing Liu Hui's Commentaries on the 'Arithmetic in Nine Sections', the author of this article came to find that early before Liu Hui, a distin- guished Mathematician during the period of Three Kingdoms (A.D.220-265), the ancient Chinese mathematicians had already developed the concept of the surds as well as grasped some basic principles of radical operations. Liu Hui wrote his commentaries in the year 263 A.D. and this exposition marked a surprising milestone in the history of Chinese Mathematics indeed.