英语必修五课文翻译FINDING THE SOLUTION.doc

原文：FINDING THE SOLUTION          Do you like puzzles? Euler did. Did you solve the one you heard for the listening task? No! Well, don't worry, Euler didn't either! As he loved mathematical puzzles, he wanted to know why this one wouldn't work. So he walked around the town and over the bridges of K6nigsberg several times. To his surprise, he found that he could cross six of the bridges without going over any of them twice or going back on himself (see Fig 3), but he couldn't cross all seven. He just had to know why. So he decided to look at the problem another way.           He drew himself a picture of the town and the seven bridges like the one above. He marked the land and the bridges. Then he put a dot or point into the centre of each of the areas of land. He joined these points together using curved lines to go over the bridges (see Fig 1). He noticed that some points had three lines going to them (A, B and C) and one had five (D). He wondered if this was important and why the puzzle would not work. As three and five are odd numbers he called them "odd" points. To make the puzzle clearer he took away the bridges to see the pattern more clearly (see Fig 2).    He wondered whether the puzzle would work if he took one bridge away (as in Fig 3). This time the diagram was simpler (as in Fig 4). He counted the lines going to points A, B, C and D. This time they were different. Two of them had even numbers of lines (B had two and D had four). Two and four are both even numbers so Euler called them "even" points. Two points in Fig 4 had an odd number of lines going to them (A and C both had three) and so he called them "odd" points.    Using this new diagram Euler started at point A, went along the straight line to B and then to C. Then he followed the curved line through D and back to A. Finally he followed the other curved line from A back through D to C where he finished the pattern. This time it worked. He had been able to go over the figure visiting each point but not going over any line twice or lifting his pencil from the page. Euler became very excited. Now he knew that the number of odd points was the key to the puzzle. However, you still needed some even points in your figure if you wanted it to work. So Euler looked for a general rule:           If a figure has more than two odd points, you cannot go over it without lifting your pencil from the page or going over a line twice.           Quickly he went to his textbooks to find some more figures. He looked at the four diagrams shown below and found that when he used his rule, he could tell if he could go over the whole figure without taking his pencil from the paper. He was overjoyed. He did not know it but his little puzzle had started a whole new branch of mathematics called "topology". In his honour this puzzle is called "finding the Euler path". 译文：寻找解决的方法你喜欢谜题吗?欧拉喜欢。

你有没有解决一个你听到的任务?不!嗯,别担心,欧拉也一样!因为他热爱数学难题,他想知道这个为什么不行所以他绕着小镇,在哥尼斯堡桥梁反复走了好几次令他吃惊的是,他发现,他可以一次性穿过六座桥在一座桥不走两次或走回头路的情况下(见图3),但是他却不能穿过所有的七座他只想知道为什么所以他决定换一种方式看这个问题 他把镇子和七个桥画在画上并标志了土地和桥梁然后他在每个地区的土地上打点他将点通过桥梁用曲线连在一起 (请参阅图1)他注意到一些点只要三条线通过(A,B和C)另一个有五条线经过(D)他想这是否重要,并且想知道为什么这样不行三加五是奇数，他称他们为“奇数的”点为了使谜题更加清晰，他擦去了桥使模式变得清晰(见图2) 他想知道如果他去掉一个桥这个难题是否将解开 (如图3)这一次的图更简单些(如图4),他数了数连接点A,B,C和d 的线.这一次不同了其中两个线变了(B有两个和D有四个)2和4都是偶数，所以欧拉称他们为“偶数的”点在图4有两个点的连线是奇数(A和C都有三个),所以他称他们为“奇数的”点 使用这个新的图，欧拉从A点开始，沿着直线到B,然后到C然后他跟着曲线通过D并回到A 。

最后他通过另外的曲线从D到C,这一次它完成模式了他已经能够通过图上的每个点，但不会通过任何一条线两次或将铅笔离开纸面欧拉变得非常兴奋现在他知道奇数的点是拼图的关键但是, 如果你想要完成，你的图仍然需要一些偶数点所以欧拉寻找到一个一般规则:如果一个图有超过两个奇数的点,你不抬起铅笔或通过一条线两次不能完成 很快他去他的课本找到更多的数据他看了看下面四个图,发现当他利用他的规律,他可以告诉他是否可以不将铅笔离开纸而通过整个图他喜出望外他不知道,但他的这个小难题已经发展一个全新的叫做“拓扑”的数学分支为了纪念他，这个谜题被称作是“寻找的欧拉路径”。