Finding The Solution Do you like puzzles?Euler did.Did you solve the one you heard for the listening task?No!Well,do not worry,Euler did not either!As he loved mathematical puzzles,he wanted to know why this one would not work.So he walked around the

Finding The Solution Do you like puzzles?Euler did.Did you solve the one you heard for the listening task?No!Well,do not worry,Euler did not either!As he loved mathematical puzzles,he wanted to know why this one would not work.So he walked around the
Finding The Solution
Do you like puzzles?Euler did.Did you solve the one you heard for the listening task?No!Well,do not worry,Euler did not either!As he loved mathematical puzzles,he wanted to know why this one would not work.So he walked around the town and over the bridges of Konigsberg several times.To his surprise,he found that he could cross six of the bridge without going over any of them twice or going back on himself(see Fig 3),but he could not 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 going to them(A,B and C) and one had five(D).He wondered if this was importand 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 Band then to C.Then he followed the curved line through D and back to A.Finally he followed the ofther 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 gong 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" .
英语翻译,不要翻译机器,我都试过的……用人脑翻译,看完以后大体说一下就可以了,让我明白,

Finding The Solution Do you like puzzles?Euler did.Did you solve the one you heard for the listening task?No!Well,do not worry,Euler did not either!As he loved mathematical puzzles,he wanted to know why this one would not work.So he walked around the
找到解决问题的方法
你喜欢难题呢?欧拉所做的.你解决你听到的任务吗?听不!哦,别担心,欧拉没有!因为他热爱数学难题,他想知道为什么这一不工作所以他走在城里,在桥梁的Konigsberg好几次了.但是令他吃惊的是,他发现他能穿过六座桥的任何不超过两次或回头路(见图3),但他不能穿过所有的7 .他刚刚知道为什么.所以他决定去看这个问题的另一种方式.
他画了自己的一幅图画和七个城镇的桥梁.他的土地和桥梁.然后他把一个网点或点到市中心的每个领域的土地.他加入了这些点数一起去他们用弯曲的线条,B和C()和一个有五个(D).他想知道这是重要的,为什么这个难题就不会发挥作用.三加五是奇数耶稣叫他们“古怪”分.让他拿走的拼图清晰的沟通桥梁的模式更清楚地看到了(见图2).
他不知道她是否会困惑的工作,如果他把一个桥走(图3).这一次的图表是简单的(图4)计算了线路将分乙、丙、d,这一次他们是不同的他们两个还编号的线(B有两个和D有四个)来和四个都是双数所以欧拉称其为“甚至”分.在图2分4个有奇数行去他们(A和C都有三个),所以他称之为“古怪”分.
利用这一新的图欧拉开始了A点,沿直线的频带然后C也跟着弧形线条经过D和回到他的ofther A终于从背部曲线D C.在那里他通过完成了这个模式.这一次它的工作.他能越过这个数字,但不能访问每点在任何线两次或解除他的铅笔从页.欧拉变得非常兴奋现在他知道这个数目的古怪的分的关键难题的.然而,你还需要一些甚至在你认为如果你想工作所以欧拉寻找一般.
如果一个数字已经超过两个奇数分时,你不能越过它没有提升你的铅笔从网页或红了一条线两次,
他很快就去找一些数字教科书…他看了看四图表,如下图所示,发现当他用他的统治,他可以告诉他是否可以越过整个轮廓不接受他的铅笔从纸他高兴极了.他不知道,但他的小拼图已经开始了一个全新的数学分支称为“拓扑" .在他的荣誉这个难题被称为“欧拉路径”发现.

5676545674567567