# 人教版英语必修五 Unit 1 Reading Speaking and Writing_图文

Unit1 Workbook

Try your best to go over the whole points of each picture without lifting your pencil from the paper or going over any line twice.
A A

D

B

D

B

C

C

Topology--Euler path

Euler

“Seven Bridges of Konigsberg” and the famous “Euler path”. What’s Euler’s puzzle?

Konigsberg is an island and there is a
river breaking here into two parts.

People wondered if they could walk around the city by crossing the seven bridges without going over any of them twice or going back on himself, but Euler found he couldn’t cross all the

seven ones. This is Euler’s puzzle.

How did Euler prepare for his research? 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, but he

couldn’t cross all seven.

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.

What are the theories? It is topology. Euler’s theory is called “The Euler path”, which is expressed like this: If a figure has more than two odd points, you can’t go over it without lifting your pencil from the page or going over a line twice. So the general rule that Euler found is the even points and the odd points .

Conclusion
Euler’s 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。

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Read the text and find out the answers to the following questions. 1. How did Euler find a problem? 2. What’s the general rule to the puzzle? 3. What branch of mathematics did Euler start?

1. How did Euler find a problem?

When he walked around the town and over the bridges of Konigsberg, he was surprised to find that he could cross six of the bridges without going over any of them twice or going back on himself, but he couldn’t cross all seven.

2. What’s the general rule to the puzzle? If a figure has more than two odd points, you can’t go over it without lifting your pencil from the page or going over a line twice. 3. What branch of mathematics did Euler start?

He started a whole new branch of mathematics called “topology”.

Fill in the chart after reading the text. How many bridges could Euler cross without going across any of them twice? How did he try to solve the puzzle? What is an “odd” point? Six

By turning the map into a diagram. One which has an odd number of lines going to it.

How many odd points are there in Fig 2 on page 45? How many odd points are there in Fig 4 on page 45?

Four

Two

What is Euler’s rule?

If a figure has more than two odd points, you cannot go over it without lifting your pencil from the page or without going over a line twice.
Yes

Did his rule work with Figs 2 and 4?

Look at the following pictures. Check to see if you are right by using a pencil to go over the diagram. Remember not to miss any points or go over any line twice. Give a reason if there is no path.

In pairs discuss the life and work of any scientist that you know. Explain their achievements and recount stories that show interesting aspects of their character and their work. Talk about how they achieved their success.

Was it because of his / her talent, intelligence, hard work, persistence, confidence, curiosity, enthusiasm or luck?

Prepare to give a talk on your chosen
scientist to the class.

The following questions may help you with your discussion. 1.Who is the scientist you admire most? 2. What nationality is this scientist? 3.What kind of family did he/she come from? 4.What kind of education did he/she receive? 5.What did he/she achieve in his/her scientific work? 6. Why did he/she achieve great success?

Writing
Now write a report about your scientist, his/ her life, achievements and the key to his / her success. Before you begin to write, remember to put your information under three headings:
Life Achievements Key to success.

Please plan your report according to these steps: Introduction to the scientist, including dates, where he / she lived and worked and which branch of science; Life of the scientist; Achievements of your chosen scientist; Key to his / her success; General summary of his/her importance in science and why you chose him/her.

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