EXERCISES

Professor: OK, before we continue, does anybody have a question? Oh, lots of questions, I see. OK, we'll go one at a time. Yes?

Student: Thank you. You talked about Fibonacci numbers in the lecture. Sorry, I don't understand. Can you explain?

Professor: Of course. What do you want to know?

Student: OK … I hope this isn't a silly question, but what does Fibonacci actually mean?

Professor: No question is ever silly – it's always good to ask. OK, it's the name of a person. Fibonacci was a European mathematician in the Middle Ages.

Student: Ah, OK. Thanks. So, we know he was a person, but what are the Fibonacci numbers? I don't get it.

Professor: The Fibonacci numbers are a sequence of numbers. They go 1, 1, 2, 3, 5, 8 and so on. Do you see the sequence? Do you see how it works?

Student: I'm not sure.

Professor: OK. This is how it works. The first number is 1, then 1 again, then 2. The third number is the first number plus the second number. The fourth number is the second number plus the third number: 1 plus 2 is 3. The fifth number is the third number, 2, plus the fourth number, 3. So the fifth number in a Fibonacci sequence is 5.

Student: Ah! I think I understand now. But what about their importance? You said these were very important.

Professor: Yes, let me explain. This sequence of numbers is important because we see it in many things. Fibonacci numbers are common in geometry, they are common in nature, for example in plants. We see the sequence everywhere.

Student: Could you give us some more examples?

Professor: OK ... well, we don't have time right now but I can bring more examples in for next class, OK?

1.

Man: It’s brilliant what they’ve done to improve the track, isn’t it? It’s faster and there’s more room for overtaking. Everyone was there to have fun and that made for a great feeling in the crowd [1].

Woman: It was a wonderful day out. It’s such a thrill to see and hear the cars. The race itself was less exciting than I’d been expecting but the mood of the spectators made up for it [1]. It was a bit difficult to find the exit though. They need more signs to show how to find the car park when you’re leaving.

Man: Hm, we did get a bit stuck in the crowd on our way out.

2.

Man: After losing an important match, as a coach, you go over and over what went wrong. You wonder if the players had had enough training beforehand. In this case, they’d been training every day for months. Physically they should have been strong and fast enough to win, but the pressure and expectations make it difficult sometimes. I reckon they had so many thoughts going through their minds that they weren’t thinking about the game itself, but more about winning the cup [2]. That led to some crucial mistakes that allowed the other team to score even though they were probably the weaker side when it comes to fitness.

3.

Woman: Have you been playing your new computer game? What do you think of it?

Boy: Actually it’s quite hard to get the hang of. The way it operates, it takes an awful lot of practice. There are so many stages before you really understand how to play it well, but that’s the whole point. Some people don’t find that very interesting, but for me that’s the fun of it, trying to work out how to beat the game if you know what I mean. The worst thing is, it costs far more than I reckon it’s worth [3]. Probably because of all the TV advertising.

4.

Woman: It was fascinating judging the Young Poet of the Year Award. It seems many young poets today are putting aside traditional dreamy views of trees, flowers and rivers in order to tackle more everyday life topics. As you might expect, some of them showed great ability in seeing the funny side of life and dealing with it in an amusing way. When discussing the poems as judges, we discovered something remarkable. Of the 150 finalists, at least twenty had more than one poem; one, more than a dozen [4]. We weren’t judging one-offs, we were looking at young poets who wrote all the time and continuously developed their work.

5.

Man: When I finished college I decided to go travelling on my own around Europe. We lived in a small town and I’d only ever been on a few short trips abroad with my family before. Anyway, I’d been planning the trip for some time, but hadn’t told my parents because I thought they’d be anxious thinking something could go wrong. When I finally announced the news to them, much to my amazement, they just sat down and spent the rest of the evening looking at maps and giving me advice about what to take [5]. I’d been wondering if they would explode furiously and tell me I couldn’t go.

6.

Woman: Caring for people is hard work, but you’re giving people something they need. You never know what’s going to happen – every day on the ward is different and you meet loads of different types of people. Most, but not all, are pleasant to deal with so being friendly but calm is a vital quality. There are plenty of options about the type of people you work with, so some deal with young children, or others prefer the elderly patients. One thing is the shifts –

you often have to work weekends and nights, but the schedules are quite flexible and you can earn more [6].

7.

Man: The trip took three days and although I could have got there in about two hours by plane it wouldn’t have been such fun. A lot of people think speeding down a motorway for hours on your own is boring, but it’s the feeling of being a part of the environment that I love. Having passengers around you talking and eating is something I’d rather avoid. You can get a bit sick of wearing a crash helmet all day, but what I spent on that and my other protective gear was worth it – when night fell, the wind got very bitter and I saved on fuel in the end [7].

8.

Man: Do you listen to the radio much?

Woman: Not usually, but in fact I woke up this morning to the sound of my mum’s playing in the background and I really got into the programme that was on.

Man: What was it?

Woman: There was a discussion on about building and construction and I got hooked right away, even though the subject isn’t particularly relevant to me or my life. There were some real experts talking about it and even the presenter seemed impressed by their knowledge of the subject. [8] It’s funny how interesting something can be even though you wouldn’t expect it to be.

Interviewer: Today I’m talking to 21-year-old, long-distance runner Ann Brown, who’s just returned from the World Championships. So, Ann, how did you feel about your performance in the championships?

Ann: When you haven’t raced for a while, you’ve no idea whether you’re in sufficiently good shape. I’d only had a few weeks of training behind me so I wasn’t thinking I’d do brilliantly, and it certainly would’ve been amazing to come first. Anyway, I was happy to get the silver medal. [24] It was an exciting race and the crowd was fantastic.

Interviewer: So what‘s your training routine like, Ann?

Ann: I do around 25 to 30 hours a week, mostly long-distance, steady stuff. I go running through the woods. Running on roads is pretty dull so I make sure there’s always some attractive countryside to keep me interested. [25] I get pleasure from seeing the changes in nature, but I do have to remember to keep my eye on the time so I can check my pace. It’s vital to keep pushing myself to my limits.

Interviewer: Do you train every day or do you take a day off?

Ann: The accepted idea is that all professional sportspeople should have at least one rest day a week, so the body can recover. I’m not a great believer in that though. At my age I find I can keep going without one. [26] I do five hours a day and I’d even like to be able to do more than that, but I don’t want to push my body too hard, because that can lead to other problems.

Interviewer: What about your competitors in races – do you get to know them as friends?

Ann: I race against athletes from all sorts of places. I wouldn’t say I’ve got friendships with them, though I’m sure some of them are really good guys, but I tend to keep a professional distance. It’d be too easy to let friendships start interfering with the way I run races. [27] Of course, at my age chatting about life, having fun and a good social life are important to me. I share a house with three mates. They’re the people I really get on well with.

Interviewer: So do you have any favourite free time activities?

Ann: Let me think. I suppose I did when I was a kid but I’m not so sure nowadays. Yeah, I used to take my kite to the top of the hills and fly it for hours. In season, skiing’s something that I get into quite a bit when I’ve got the time. [28] I’ve always enjoyed active things, and never really been much of a reader of books or that kind of thing. Of course, I watch TV and play computer games like most people.

Interviewer: And do you get recognised in the street very often?

Ann: Very rarely, I’m pleased to say, as I think it’d be a bit strange and I’m not sure how comfortable I’d feel about being stopped for autographs and pictures all the time. On the whole I find people wanting your autograph a bit of a pain to be honest. [29] It happens sometimes when I’m at events and at first you say OK, and then after a while you wish it’d stop. I suppose I did that sort of thing when I was younger. It was always such a thrill to meet someone in the public eye.

Interviewer: So are you planning for the next Olympics?

Ann: Well, in my sport most people peak in their late twenties so it’s important to have an eye on the next five years or so, cos that’s when supposedly I’ll be at my best. [30] In the immediate future I want to do well of course but I’m concentrating my attention further ahead. Fortunately, I’ve been injury-free so far – so I don’t have that worry. It’s no use having fantasies about winning gold medals until I’ve reached the top of my own fitness and endurance levels. Then I can start to think seriously about it.