课文1—AB数学专业英语翻译(第二版)吴炯圻

2-A Why study geometry?Why do we study geometry? The student beginning the study of this text may well ask, "What is geometry? What can I expect to gain from this study?2-A为什么研究几何学？为什么我们研究几何学？刚开始学习这篇文章的学生会疑问，“几何是什么？研究几何我们能学到什么呢？Many leading institutions of higher learning have recognized that positive benefits can be gained by all who study this branch of mathematics. This is evident from the fact that they require study of geometry as a prerequisite to matriculation in those schools.许多居领导地位的学术机构承认，所有学习这个数学分支的人都将得到很好的收益。

事实是，他们需要学习几何作为学校入学考试的先决条件。

Geometry had its origin long ago in the measurements by the Babylonians and Egyptians of their lands inundated by the floods of the Nile River. The greek word geometry is derived from geo, meaning "earth," and metron, meaning "measure." As early as 2000 B. C. we find the land surveyors of these people reestablishing vanishing landmarks and boundaries by utilizing the truths of geometry.很早以前，几何学源于测量被尼罗河的洪水淹没了的巴比伦人和埃及人的土地。

2.4 整数、有理数与实数4－A Integers and rational numbersThere exist certain subsets of R which are distinguished because they have special properties not shared by all real numbers. In this section we shall discuss such subsets, the integers and the rational numbers.有一些R 的子集很著名，因为他们具有实数所不具备的特殊性质。

在本节我们将讨论这样的子集，整数集和有理数集。

To introduce the positive integers we begin with the number 1, whose existence is guaranteed by Axiom 4. The number 1+1 is denoted by 2, the number 2+1 by 3, and so on. The numbers 1,2,3,…, obtained in this way by repeated addition of 1 are all positive, and they are called the positive integers.我们从数字 1 开始介绍正整数，公理 4 保证了 1 的存在性。

1+1 用2 表示，2+1 用3 表示，以此类推，由 1 重复累加的方式得到的数字 1,2,3，…都是正的，它们被叫做正整数。

Strictly speaking, this description of the positive integers is not entirely complete because we have not explained in detail what we mean by the expressions “and so on”, or “repeated addition of 1”.严格地说，这种关于正整数的描述是不完整的，因为我们没有详细解释“等等”或者“1的重复累加”的含义。

Unit 1Section BCulture ShockDo you think studying in a different country is something that sounds very exciting? Like many young people who leave home to study in another country, do you think you would have lots of desirable fun? Certainly, it is a new experience, which brings the opportunity of discovering fascinating things and a feeling of freedom. In spite of these advantages, however, there are also some challenges you will encounter. Because your views may clash with the different beliefs, norms, values, and traditions that exist in different countries, you may have difficulty adjusting to a new culture and to those parts of the culture not familiar to you. This is culture shock. Evidently, at least four essential stages of culture-shock adjustment occur.The first stage is called "the honeymoon". In this stage, you feel excitement about living in a different place, and everything seems to be marvelous. You like everything, and everybody seems to be so nice to you. Also, the amusement of life in a new culture seems as though it will have no ending.Eventually, however, the second stage of culture shock appears. This is the "hostility stage". You begin to notice that not everything is as good as you had originally thought it was. You become tired of many things about the new culture. Moreover, people don't treat you like a guest anymore. Everything that seemed to be so wonderful at first is now awful, and everything makes you feel distressed and tired.Usually at this point in your adjustment to a new culture, you devise some defense mechanisms to help you cope and to protect yourself against the effects of culture shock. One type of coping mechanism is called "repression". This happens when you pretend that everything is acceptable and that nothing bothers you. Another type of defense mechanism is called "regression". This occurs when you start to act as if you are younger than you actually are; you act like a child. You forget everything, and sometimes you become careless and irresponsible. The third kind of defense mechanism is called "isolation". You would rather be home alone, and you don't want to communicate with anybody. With isolation, you try to avoid the effects of culture shock, or at least that's what you think. Isolation is one of the worst coping mechanisms you can use because it separates you from those things that could really help you. The last type of defense mechanism is called "rejection". With this coping mechanism, you think you don't need anybody. You feel you are coping fine alone, so you don't try to ask for help.The defense mechanisms you utilize in the hostility stage are not helpful. If you only occasionally use one of these coping mechanisms to help yourself survive, that is acceptable. You must be cautious, however. These mechanisms can really hurt you because they prevent you from making necessary adjustments to the new culture.After you deal with your hostile feelings, recognition of the temporary nature of culture shock begins. Then you come to the third stage called "recovery". In this stage, you start feeling more positive, and you try to develop comprehension of everything you don't understand. The whole situation starts to become more favorable; you recover from the symptoms of the first two stages, and you adjust yourself to the new norms, values, and even beliefs and traditions of the newcountry. You begin to see that even though the distinctions of the culture are different from your own, it has elements that you can learn to appreciate.The last stage of culture shock is called "adjustment". In this stage, you have reached a point where you actually feel good because you have learned enough to understand the new culture. The things that initially made you feel uncomfortable or strange are now things that you understand. This acquisition of understanding alleviates much of the stress. Now you feel comfortable; you have adjusted to the new culture.Evidently, culture shock is something you cannot avoid when living in a foreign country. It does not seem like a very helpful experience when you are going through its four stages. However, when you have completely adjusted to a new culture you can more fully enjoy it. You learn how to interact with other people, and you learn a considerable amount about life in a culture that is not your own. Furthermore, learning about other cultures and how to adjust to the shock of living in them helps you learn more about yourself.Words: 753。

第一章：数学方程与比例1-A 什么是数学数学来自于人的社会实践，例如，工业和农业生产、商业活动、军事行动和科研工作。

与数学反过来，为实践服务和所有字段中的伟大作用。

没有现代的科学和技术分支机构可以定期制定中的数学，应用无早有需要的人来了数字和形式的概念。

然后，开发出的几何土地和三角测量的问题来自测量的问题。

若要对付一些更复杂的实际问题，男子成立，然后解决方程未知号码，因此代数发生。

17 世纪前, 男子向自己限于小学数学，即几何、三角和代数，只有常量被认为在其中。

17 世纪产业的快速发展促进了经济和技术的进展和所需变量的数量、处理从常量到带来两个分支的数学-解析几何和微积分，属于高等数学，现在有很多分支机构，其中有数学分析、高等代数、微分方程的高等数学中的可变数量的飞跃函数理论等。

数学家研究理念和主张。

所有命题公理、假设、定义和定理都。

符号是一种特殊和功能强大的数学工具，用于表示很多时候的理念和主张。

公式、数字和图表是阿拉伯数字1,2,3,4,5,6,7,8,9,0 与另外的符号"+"、减法"-"，乘"*"，除"\"和平等"="。

数学中的结论得到主要由逻辑推理和计算。

长期的数学史上，以中心地点的数学方法被占领逻辑扣除。

现在，由于电子计算机是迅速发展和广泛应用，计算的作用变得越来越多重要。

在我们这个时代计算不只用于处理大量的信息和数据，而且还进行一些只是可以做的工作较早前的逻辑推理，例如，大部分的几何定理的证明。

1--B 方程方程是平等的语句的两个相等的数字或数字符号之间。

因此(a-5）= 一5a 和x 3 = 5 是方程。

方程的两种——身份和方程的条件。

方程的算术或代数的身份。

这种方程中两名成员是相似的或成为相似的指示操作的性能。

因此12-2=2+8,(m+n)(m-n) = m n 是身份。

1—c 比与测量今天的思想沟通往往根据编号和数量的比较。

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。

New Words & Expressions:algebra 代数学geometrical 几何的algebraic 代数的identity 恒等式arithmetic 算术, 算术的measure 测量，测度axiom 公理numerical 数值的, 数字的conception 概念，观点operation 运算constant 常数postulate 公设logical deduction 逻辑推理proposition 命题division 除，除法subtraction 减，减法formula 公式term 项，术语trigonometry 三角学variable 变化的，变量2.1 数学、方程与比例Mathematics, Equation and Ratio4Mathematics comes from man’s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches.1－A What is mathematics数学来源于人类的社会实践，比如工农业生产，商业活动，军事行动和科学技术研究。

And in turn, mathematics serves the practice and plays a great role in all fields. No modern scientific and technological branches could be regularly developed without the application of mathematics.反过来，数学服务于实践，并在各个领域中起着非常重要的作用。

1－A What is mathematicsMathematics comes from man’s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches. And in turn, mathematics serves the practice and plays a great role in all fields. No modern scientific and technological branches could be regularly developed without the application of mathematics.数学来源于人类的社会实践，比如工农业生产，商业活动，军事行动和科学技术研究。

反过来，数学服务于实践，并在各个领域中起着非常重要的作用。

没有应用数学，任何一个现在的科技的分支都不能正常发展。

From the early need of man came the concepts of numbers and forms. Then, geometry developed out of problems of measuring land , and trigonometry came from problems of surveying . To deal with some more complex practical problems, man established and then solved equation with unknown numbers ,thus algebra occurred. Before 17th century, man confined himself to the elementary mathematics, i.e. , geometry, trigonometry and algebra, in which only the constants are considered.很早的时候，人类的需要产生了数和形式的概念，接着，测量土地的需要形成了几何，出于测量的需要产生了三角几何，为了处理更复杂的实际问题，人类建立和解决了带未知参数的方程，从而产生了代数学，17世纪前，人类局限于只考虑常数的初等数学，即几何，三角几何和代数。

7A在日常使用的英文单词"序列"和' '系列"是同义词，和他们用来建议一系列的事情或按某种顺序排列的事件。

在数学中，这句话有特别技术的意义。

"序列"一词被受雇如在共同使用这一术语，传达的理念的一套东西排列顺序，但"系列"一词用于稍有不同的意义。

概念在本节中，将讨论序列和系列将定义第11 节。

如果为每个正整数n 有关联的真实或复数a，那时有序的集据说是定义一个无限的序列。

这里最重要的是每个成员集的已标记的整数，使我们可以发言的第一届、第二个任期，以及，一般的第n 个词。

每个学期了继任者，因此，没有任何"最后"一词。

如果我们给一些规则或第n 个词描述的公式，可以构造序列的最常见的例子。

因此，例如，公式= 1 定义的序列的第五个任期是1.有时两个或多个公式可受雇作为，例如，a=1.the 第一次在这种情况下被1 的一些术语。

另一种常见方法定义一系列是一套的说明解释了如何在一个给定的开始后进行的。

因此，我们可能= 1。

此特定的规则被称为递归公式，它定义了著名的序列，其条款被称为斐波那契数。

第一次的几个术语are1。

最重要的事情是序列的序列的这样f(n) 的每个n=1.In 事实的第n 个燕鸥是序列的序列的正整数上定义一些函数 f 的任何序列，这可能是序列的序列的最方便的方法，国家技术定义。

定义。

其域是所有积极integers1 的一组函数f 称为一个无限的序列。

函数值f(n) 调用序列的第n 个词。

通过按顺序，因此编写条款通常显示的功能（即，函数值的集合）的范围：f (2)。

为简便起见，{f(n)} 符号用于指示第n 个任期是f(n) 的序列。

由使用下标，很多时候表示，n 的依赖和我们写，或类似的而不是f (n0。

除非另外指定，否则所有的序列，在这一章中假定有真实的或复杂的条款。

7B我们担心在这里主要的问题在于决定是否条款f(n) 倾向于有限的n 无限增加。