1、人教课标 高二 必修 5 Unit 1,Reading task,on Page 44,Unit 1 Great scientists,Whats Eulers puzzle?Koningsberg is an island and there is a river breaking it into two parts.,“Seven Bridges of Konigsberg” and the famous “Euler path”.,People wondered if they could walk around the city by crossing the seven bridge
2、s without going over any of them twice or going back on himself, but Euler found he couldnt cross all the seven ones. This is Eulers puzzle.,The first stage in his research is to find the problem that he could cross six of the bridges without going over any of them twice or going back on himself, bu
3、t he couldnt cross all seven.,How did Euler prepare for his research?,The second stage is to think of a method: He drew a map and used dots and lines to simplify his analysis. Trying and observing over and over again, he found a general rule.,It is topology. Eulers theory is called “The Euler path”,
4、 which is expressed like this: 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.,What are the theories?,So the general rule that Euler found is the even points and the odd points.,Look at the following pictures:,ConclusionEulers theory (一笔画)可以一笔画只有两种情况：1. 没有奇数顶点。2. 只有两个奇数顶点。,