I need this translated if anyone knows what it means, i asked some of my friends who can read Chinese but they weren't sure what it means. It's from the 3rd century, so don't be ashamed if you can't read it.


更相減損術

更相减损术是出自《九章算术》的一种求最大公约数的算法，它原本是为约分而设计的，但它适用于任何需要求最大公约数的场合。
　　《九章算术》是中国古代的数学专著，其中的“更相减损术”可以用来求两个数的最大公约数，即“可半者半之，不可半者，副置分母、子之数，以少减多，更相减损，求其等也。以等数约之。” 　　翻译成现代语言如下： 　
　第一步：任意给定两个正整数；判断它们是否都是偶数。若是，则用2约简；若不是则执行第二步。
　第二步：以较大的数减较小的数，接着把所得的差与较小的数比较，并以大数减小数。继续这个操作，直到所得的减数和差相等为止。 　　
则第一步中约掉的若干个2与第二步中等数的乘积就是所求的最大公约数。 　　
其中所说的“等数”，就是最大公约数。求“等数”的办法是“更相减损”法。


实例
　　例: 用更相减损术求98与63的最大公约数。 　　解：由于63不是偶数，把98和63以大数减小数，并辗转相减： 　　98-63=35 　　63-35=28 　　35-28=7 　　28-7=21 　
　21-7=14 　　14-7=7 　　所以，98和63的最大公约数等于7。

I do not understand chinese, but I was able to use google for a rough translation, and this seems to be the correct context... you probably search the internet for it lol, it is an algorithm that was described in a commentary by Liu Hui on the nine chapters on the mathematical art, about a method to find the gcd of two numbers... but I want to know what the method or algorithm would be called in english (更相減損術), google doesn't give a great translation of this, google translates it as "More impaired patients compared" which doesn't make sense

This post was edited by CornMuffin on Apr 5 2011 11:06pm

As far as I know, this technique does not have a literal English translation.

A vague term to describe it in English would be: "cross over and simplify" or something of the sort.
I was taught how to use it in Chinese so... but haven't seen it used in the West (from what I've came across).

alright, thanks

CHING CHONG LING LONG http://www.youtube.com/watch?v=Johj5WEYzZo

This was the answer:
http://www.youtube.com/watch?v=uMVKmItZP7c&feature=watch_response