《天文学家》PPT课件.pptVIP

Answer key for Exercise 1: Students will give their own answers which may very. Answer key for Exercise 3: Tick all symbols except angle. Listening Task on page 44 Answer key for Exercise 4: topology euler’s new branch of mathematics Why Euler is considered to be a great mathematician introduced many new symbols into maths wrote more books than anyone before or since discovered a new branch of mathematics Suggest answers to Exercise 5: It had a river running through it. The centre of konigsberg is an island and as it passes the island the river breaks into two parts. Seven bridges were built so that the people of the city could get from one part to another. The people wondered if you could walk around the city so that you would cross each bridge only once. Suggested answers to Exercise 6: There is no Euler path for this figure. Look at Figure 4 in the Reading task. It is a Euler path for Figure 3. A MATHEMATICIAN’S PROBLEM John Smith (JS) is talking to Zhao Yang (ZY) about a mathematician who interests him. Part 1 JS: Do you know that we’ve been studying Euler in maths? ZY: Who is he? I’ve never heard of him. JS: Well, he was a famous mathematician in the eighteenth century. He revised all the pure mathematics that was know in his day. ZY: That probably wasn’t very much. JS: You’re wrong there. He wrote more than any other mathematician before or since. ZY: Really! Well, what did he do? JS: He introduced a lot of symbols into mathematics such as pi and the terms sine and cosine. ZY: Wow! JS: And he did half of this work when he was blind. ZY: How did he do that? JS: He told his ideas to someone else who wrote them down. Part 2 ZY: What were his achievements? JS: He introduced a new branch of mathematics called topology. It helps you understand things by using diagrams. The subway map is a good example. It doesn’t tell you distances but it shows how stations connect together. ZY: How did he start topology? JS: Well, in 1735 he was inspired by a problem in the city o