普通高中课程标准实验教科书 英语必修5 Unit 1 Great scientists

 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 mathematical¹ 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 Fig² 3), but he couldn't cross all seven. He just had to know why. So he decided³ 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 curved⁴ 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 odd⁵ 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 diagram⁶ 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 diagrams⁷ 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 mathematics⁸ called "topology". In his honour this puzzle is called "finding⁹ the Euler path".

  

1 mathematical   

adj.数学的，数学上的

参考例句：

• The solution can be expressed by a mathematical equation.答案可用一个数学方程式来表示。
• Einstein was a mathematical genius.爱因斯坦是数学天才。

2 fig   

n.无花果(树)

参考例句：

• The doctor finished the fig he had been eating and selected another.这位医生吃完了嘴里的无花果，又挑了一个。
• You can't find a person who doesn't know fig in the United States.你找不到任何一个在美国的人不知道无花果的。

3 decided   

adj.决定了的，坚决的；明显的，明确的

参考例句：

• This gave them a decided advantage over their opponents.这使他们比对手具有明显的优势。
• There is a decided difference between British and Chinese way of greeting.英国人和中国人打招呼的方式有很明显的区别。

4 curved   

a.弯曲的

参考例句：

• His lips curved in a barely perceptible smile. 他的嘴角弯了弯，露出一丝几乎察觉不到的笑容。
• The missile curved gracefully towards its target. 导弹呈优美的曲线状飞向目标。

5 odd   

adj.奇特的；临时的；奇数的；n.[pl.]机会

参考例句：

• She looks a bit odd.I wonder what has happened to her.她的神色有些异样，不知出了什么事。
• He's an odd character and no mistake!他的确是个怪人！

6 diagram   

n.图表，示意图；图解；vt.绘制…的示意图

参考例句：

• On the back of the letter was a diagram.信的背面是张图表。
• The engineer drew a diagram of the bridge.工程师绘制了一幅这座桥的示意图。

7 diagrams   

图解，简图，图表( diagram的名词复数 )

参考例句：

• Don't clutter the page with too many diagrams. 别用太多的图表来堆砌版面。
• The computer reproduces the data as a set of diagrams. 电脑使这些数据再现为一系列图表。

8 mathematics   

n.（用作单）数学；（用作单或复）计算(能力）

参考例句：

• He has come out in front in the study of mathematics.他在数学方面已名列前茅。
• She is working at a difficult problem in mathematics.她在做一道数学难题。

9 finding   

n.发现，发现物；调查的结果

参考例句：

• The finding makes some sense.该发现具有一定的意义。
• That's an encouraging finding.这是一个鼓舞人心的发现。