Squaring a circle 直线画圆

FOR some it was a first encounter with algebra that turned them off; for others it was an introduction to calculus. At a certain point in their education many intelligent people have reacted with pleasure to the thought that they would never again have to sit through a maths lesson. Such folk may be bemused to discover that mathematics can be fun and that books on the subject are often bestsellers. “Here’s Looking at Euclid” was published in Britain in April under the title “Alex’s Adventures in Numberland” and is selling well.

对一些人而言,此书是首次看到使其厌烦的代数;对一些人而言,此书是微积分入门.在受教育过程中,很多聪明人在某个时刻听到不用再上数学课,会很高兴.在发现数学家很有趣,而且数学方面的书都很畅销时,他们会为此感到困惑不解.<看看欧几里德> 4月份在英国出版,并更名为<Alex探秘数学世界>依然销售火爆.

A book on maths for the general reader has to be well and enthusiastically written. It needs to stimulate the mind and illustrate the relevance and beauty of the subject. And, as much as possible, it must limit the concepts and methods that it introduces to those that a schoolchild would understand. Both “The Number Mysteries” and “Here’s Looking at Euclid” meet these criteria. Marcus du Sautoy, who in 2008 took over from Richard Dawkins as Oxford University’s professor for the public understanding of science, says that he is writing for all ages from one to 101 but he is really aiming to communicate with those whose maths is at the level of a bright, interested 11-to-14-year-old.

面对大众读者的数学方面著作,一定要文笔流畅并充满热情.它需要激发思维并展示数学的关联性和优美之处.并尽可能少的介绍关于那些学龄童都知道的概念和技巧.<数学秘闻>和<看看欧几里德>恰好符合上述要求. 接替Richard Dawkins 就职牛津大学大众科普教授Marcus du Sautoy称:他的著作适合于1到101岁的人阅读,但他的主要交流对象是11-14岁比较聪明并对数学充满兴趣的少年.

His book, subtitled “A Mathematical Odyssey Through Everyday Life”, is clearly written, attractively produced, well illustrated with drawings and diagrams, and limited to five chapters, each of which takes the reader on a journey through one of the big themes of mathematics and ends with a yet-to-be-solved million-dollar-prize puzzle. Mr du Sautoy does not shrink from exposing the reader to difficult ideas, but he gains and keeps his attention by explaining their relevance and connection to such everyday problems as filling a lorry with boxes of different sizes, employing the correct strategy to win at Monopoly, predicting the future and charting the flight of a football.

他的书的副标题是 <数学通俗概览>,文笔清晰,排版诱人,文图相间却仅有五章,每一章都带着读者经历数学中大的主题,并以悬而未决的百万大奖难题结束. du Sautoy先生并不仅打算向读者展示难题,而将更多的精力放在探索它们和日常问题之间的关系,比如用不同大小的盒子装满货车,寻找垄断中获胜的正确对策,预测未来和画出足球轨迹.
Inevitably, Mr  du Sautoy begins with prime numbamazoniaers, the delight of many mathematicians, which in common with the Fibonacci sequence and the golden ratio appear in the natural world in an astonishing variety of ways. The primes, the indivisible numbers that are the building blocks of all other numbers, crop up everywhere, from the back of David Beckham’s shirt (23) to Messiaen’s “Quartet for the End of Time” (17 and 29), to the life cycle of the North American cicada (17). Having a lifespan that is a prime number significantly reduces the chances of these insects being eaten by predators that also appear in the forest at regular intervals every few years.

不可避免的是 du Sautoy也以素数开始,这也是很多数学家的兴趣所在,自然界中常以不可想像方式出现的有斐波那契数列和黄金分割率.不可整除的数字,称为素数.它们是其它数字的基本组成部分,并随处可见,如贝克汉姆背后的号码”23” ,Messiaen的 “Quartet for the End of Time” (17和29)和北美蝉和生命周期(17).素数生命周期非常重要,它减少了蝉被每隔几年周期性出现的食肉动物吃掉的机率.

There may be a different science in other galaxies but primes are universal. In 1974 NASA directed a message towards the globular star cluster M13 consisting of a series of zeroes and ones which could be arranged to form a pixelated picture that conveys information about the planet Earth. The star cluster is 25,000 light-years away so it will be some time before a reply is received, but the number of pixels (1679 = 23 x 73) should ensure that if there is life out there the message will be understood.

在其它星球,画面虽然不同,但素数却一样.1974年,NASA向球状星系M13发射了由0和1组成的无线电信号,这些信号可以排成包含了地球信息的点阵图像.这个星系距地球25000光年,因此在收到回复之前,我们还要等上一段时间,但点阵图的像素是(1679=23X73),就保证了如果存在外星生命,它们能够理解这些信息.

A former foreign correspondent now reporting on the world of mathematics, Mr Bellos covers many of the same themes as Mr du Sautoy, at greater length but with equal gusto and readability. Beginning with an Amazonian tribe who only count to five and ending with an infinity bigger than the infinity of natural numbers, he traces the development of mathematics from its beginnings and meets modern enthusiasts such as Maki Kaji, who popularised Sudoku (“neither geeky nor formal”), who collects rubber bands and photographs car number plates. Along the way Mr Bellos explores Vedic mathematics and its arithmetical tricks; he describes how pi has been calculated to an ever-increasing number of decimal places (2.7 trillion by the end of 2009); and he explains why the super ellipse is the best shape for a roundabout and how within a randomly selected group of 23 people it is more likely than not that two will share a birthday.

以前的记者Bellos先生也报道数学界的轶闻,和 du Sautoy先生的主题相同,虽然篇幅更长,却具有同样的可读性.从只能数到5的亚马逊部落开始,以比无穷大自然数还大的数结束,他从数学起源开始,到像Maki Kaji这样的现代数学发烧者.Maki Kellipseaji被大家称为 Sudoku(“既不低俗,也不正式”),他收集橡胶带和拍摄汽车牌.这一路上,Bellos探索了古印度的数学家们和它的算法技巧;他描述了Pi是如何计算,并表示成为持续增加的十进制小数(2009年也算到了2.7万亿位),解释了为什么超椭圆是所有圆里面最好的以及由随机抽取的23人里,极有可能两个人是同一天生日.更多信息请访问：http://www.24en.com/

Those of a mathematical inclination will enjoy both these books. So too will many who never “got” the subject at school or suffered as a result of dull and uninspiring teaching. Maths is fundamental to the world we live in, and these clear, entertaining introductions to the subject deserve to be read by those prepared to put unhappy memories behind them, and discover how and why that is the case.

数学爱好者将会非常喜欢这两本书.对于那些没有在学校里获得相关知识或者遭受无聊数学教育的人而言,同样如此.数学是我们生存世界的基本组成部分,那些准备把不愉快数学学习经历抛之脑后的人,这些条理清晰,娓娓动人的数学介绍是非常值得一读的,就会发现它如何并为什么会是这么回事.