数学专业英语翻译

第一段翻译(2)：what is the exact value of the number pai?a mathematician made an experiment in order to find his own estimation of the number pai.in his experiment,he used an old bicycle wheel of diameter 63.7cm.he marked the point on the tire where the wheel was touching the ground and he rolled the wheel straight ahead by turning it 20 times.next,he measured the distance traveled by the wheel,which was 39.69 meters.he divided the number 3969 by 20*63.7 and obtained 3.115384615 as an approximation of the number pai.of course,this was just his estimate of the number pai and he was aware that it was not very accurate.

数π的精确值是什么？一位数学家做了实验以便找到他自己对数π的估计。在试验中，他用了一直径63.1厘米的旧自行车轮。他在车轮接触地面的轮胎上做了标记，而且将车轮向前转动20次。接下来，他测量了车轮经过的距离，是39.69米。他用3969除20*63.7得到了数π的近似值3.115384615。当然，这只是对数π的估计值，并且他也意识到不是很准确。

第二段翻译(5)：one of the first articles which we included in the "History Topics" section archive was on the history of pai.it is a very popular article and has prompted many to ask for a similar article about the number e.there is a great contrast between the historical developments of these two numbers and in many ways writing a history of e is a much harder task than writing one of pai.the number e is,compared to pai,a relative newcomer on the mathematical scene.

我们包括在“历史专题”部分档案中的第一篇文章就是历史上的π，这是一篇很流行的文章，也促使许多人想了解下一些有关数e的类似文章。这两个数字的历史发展中有着很大的反差并且在许多方面写数e的历史是比写π的历史更为艰巨的任务。与π相比，数e在数学界相对较晚。

第三段翻译(24)：the path to the development of the integral is a branching one,where similar discoveries were made simultaneously by different people.the history of the technique that is currently known as integration began with attempts to find the area underneath curves.the foundations for the discovery of the integral were first laid by Cavalieri,an Italian Mathematician,in around 1635.Cavalieri's work centered around the observation that a curve can be considered to be sketched by a moving point and an area to be sketched by a moving line.

积分发展的道路是一个分支，不同的人在同一时间作了类似的发现。目前众所周知的积分这一历史方法最初是为了求出曲线下方的面积。积分的的第一奠基人是Cavalieri（卡瓦列里），一位意大利数学家，时间大约为1635年。Cavalieri（卡瓦列里）的工作集中在观察，即一个曲线可以被视为是移动的点所勾勒且和面积由移动的线勾勒出。

第四段翻译(35)：Pierre De Fermat's method for finding a tangent was developed during the 1630's,and though never rigorously formulated,is almost exactly the method used bu Newton and cking a formal concept of a limit,Fermat was unable to properly justify his work.however,by examining his techniques,it is obvious that he understood precisely the method used in differentiation today. in order to understand Fermat's mathod,it is first necessary to consider his technique for finding maxima.Fermat's first documented problem in differentiation involved finding the maxima of an equation,and it is clearly this work that led to his technique for finding tangents.

找到一个切线的Pierre De Ferma（皮埃尔·德·费马）方法发展于1630，尽管从来没有严格的规定，却几乎是被Newton（牛顿）和Leibniz（莱布尼茨）完全采用的方法。缺乏一个正式的概念限制，Fermat（费马）无法严格地证明他的工作是正确的。然而，通过查看他的技术，很显然，他准确地明白今天在微分中使用的