"mathematics." Britannica Student Article “数学” 大英百科学生文章

mathematics 数学

Britannica Student Article 大英百科学生文章

Introduction 介绍

Mathematics is often defined as the study of quantity, magnitude, and relations of numbers or symbols. It embraces the subjects of arithmetic, geometry, algebra, calculus, probability, statistics, and many other special areas of research.

数学通常被定义为研究数字或符号的数量、大小和关系的学科。它包含诸如算术、几何学、代数学、微积分学、概率、统计学等学科，还有其它许多特殊的研究领域。

There are two major divisions of mathematics: pure and applied. Pure mathematics investigates the subject solely for its theoretical interest. Applied mathematics develops tools and techniques for solving specific problems of business and engineering or for highly theoretical applications in the sciences.

数学有两个主要的分支：纯粹数学和理论数学。纯粹数学（理论数学）研究的课题仅仅是出于它的理论价值。应用数学则研发出工具和技术，为了解决那些商业、工程或是科学中高阶理论应用方面的具体问题。

Mathematics is pervasive throughout modern life. Baking a cake or building a house involves the use of numbers, geometry, measures, and space. The design of precision instruments, the development of new technologies, and advanced computers all use more technical mathematics.

数学遍及现代生活的方方面面。烤块蛋糕或是建造房屋都包括数字、几何、测量和空间的运用。精密仪器的设计，新技术的发展，还有先进的计算机都越来越多的使用到专业数学知识。

HISTORY 历史

Mathematics first arose from the practical need to measure time and to count. Thus, the history of mathematics begins with the origins of numbers and recognition of the dimensions and properties of space and time. The earliest evidence of primitive forms of counting occurs in notched bones and scored pieces of wood and stone. Early uses of geometry are revealed in patterns found on ancient cave walls and pottery.

数学最初是从度量时间并进行计算的实际需求中诞生的。因此，数学的历史，首先是数字的起源，是从对时空尺度与性质的认识开始的。有关计算基本形式的最早证据出现在锯齿状的骨头和有刮痕的木片石片上。而那些被发现于古穴石壁和陶器上的图案，则显示了几何学的最先运用。

Ancient Periods 古代

As civilizations arose in Asia and the Near East, the field of mathematics evolved. Both sophisticated number systems and basic knowledge of arithmetic, geometry, and algebra began to develop.

随着文明在亚洲和近东地区的出现，数学领域也逐渐形成。精密的数字体系和基本的算术知识，几何学还有代数学开始发展起来。

Egypt and Mesopotamia. 埃及和美索不达米亚

The earliest continuous records of mathematical activity that have survived in written form are from the 2nd millennium BC. The Egyptian pyramids reveal evidence of a fundamental knowledge of surveying and geometry as early as 2900 BC. Written testimony of what the Egyptians knew, however, is known from documents drawn up about 1,000 years later.

最早关于数学活动的连续记录以书面的形式从公元前两千年被保存至今。埃及金字塔显示了作为公元前2900多年运用测量和几何学基本知识的证据。有关埃及人拥有知识的书面证据[？]……

Two of the best-known sources for our current knowledge of ancient Egyptian mathematics are the Rhind papyrus and the Moscow papyrus. These present many different kinds of practical mathematical problems, including applications to surveying, salary distributions, calculations of the areas of simple geometric surfaces and volumes such as the truncated pyramid, and simple solutions for first- and second-degree equations.

我 们目前关于古埃及数学的认识来源于两个流传最久远的纸莎纸卷轴，它们是 Rhind 卷轴和 Moscow 卷轴。这些卷宗呈现出许多不同种类的实用数学问题，其中包括测量中数学的应用，发放薪金，计算像截棱锥这样简单的几何表面积的体积，还有简单的一次二次方 程式解法。

Egyptian arithmetic, based on counting in groups of ten, was relatively simple. Base-10 systems, the most widespread throughout the world, probably arose for biological reasons. The fingers of both hands facilitated natural counting in groups of ten. Numbers are sometimes called digits from the Latin word for finger. In the Egyptians' base-10 arithmetic, hieroglyphs stood for individual units and groups of tens, hundreds, and thousands. Higher powers of ten made it possible to count numbers into the millions. Unlike our familiar number system, which is both decimal and positional (23 is not the same as 32), the Egyptians' arithmetic was not positional but additive.

埃 及基于十进制的算术相对比较简单。基于十进制的系统在全世界广泛的流传开来，也许是因为它生物学上的原因。数字有时被称为 digits ，拉丁语中表示手指或足趾的意思。在埃及人10进制的算术中，象形文字代表各个单元并依据十、百、千来组群。10进制的优越性使得百万数量的计算成为可 能。和我们熟知的十进位与位置相关的（23不同于32）数字系统不同，埃及人的算术中没有位置的区别，而仅仅是追加上去。

Unlike the Egyptians, the Babylonians of ancient Mesopotamia developed flexible techniques for dealing with fractions. They also succeeded in developing a more sophisticated base-10 arithmetic that was positional, and they kept mathematical records on clay tablets. The most remarkable feature of Babylonian arithmetic was its use of a sexagesimal (base 60) place-valued system in addition to a decimal system. Thus the Babylonians counted in groups of sixty as well as ten. Babylonian mathematics is still used to tell time—an hour consists of 60 minutes, and each minute is divided into 60 seconds—and circles are measured in divisions of 360 degrees.

与埃及人不同，美索不达米亚地区的巴比伦人发明了灵活的处理分数的技术。他们还成功的发明了更为复杂的10进制算术，并在这种算术中引入了位置的概念，并且将数学方面的记录保存在黏土板上。巴比伦人的算术最引人注目的特点是它使用了六十分数（60进位）标值系统作为十进位小数系统的补充。因此，巴比伦人将60同10一样的也计为一组。巴比伦的数学至今仍被用于表述时间——1小时由60分钟组成，1分钟又可以分成60秒——并且圆周也被分为360度。

The Babylonians apparently adopted their base-60 number system for economic reasons. Their principal units of weight and money were the mina, consisting of 60 shekels, and the talent, consisting of 60 mina. This sexagesimal arithmetic was used in commerce and astronomy. Surviving tablets also show the Babylonians' facility in computing compound interest, squares, and square roots.



Because their base-60 system was especially flexible for computation and handling fractions, the Babylonians were particularly strong in algebra and number theory. Tablets survive giving solutions to first-, second-, and some third-degree equations. Despite rudimentary knowledge of geometry, the Babylonians knew many cases of the Pythagorean theorem for right triangles. They also knew accurate area formulas for triangles and trapezoids. Since they used a crude approximation of three for the value of pi, they achieved only rough estimates for the areas of circles.



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上文皆本人译自《大英百科》，才疏学浅，愧遗错陋，望指正，不胜感激。
accason@gmail.com December, 2006