Maths everywhere
Maths everywhere

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Maths everywhere

A mathematical muse

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FRANCESCA HUNT
Saturday today. I went to the City Centre in the morning – window shopping. I looked in a music shop. Looking at the guitars, I was struck by how small the gaps between the frets get. I wonder how the makers know where to put them? Went to see friends this evening. I amused Sarah, their daughter, with my ‘think of a number’ routine. It’s the one that goes, ‘Think of a number without telling me which one; double it; add five; multiply by three; add nine; divide by six; take away the number you first thought of; and the answer’s four’. She thought it was magic that I already knew she’d got four as the answer. But the thing is, the answer will always be four. In fact, it doesn’t depend on the number she thought of at all! I suppose I could try to explain it to Sarah using algebra. But I didn’t want to destroy the spell for her. I left rather late – about one a.m. We’d got there about eight p.m. – so we’d stayed five hours. But eight and five aren’t one! And neither is one minus five, eight! Funny arithmetic clocks use. A lovely sunny Sunday afternoon. I took the dog for a walk in the park. Tried to find the age of the oak and the silver birch. I read somewhere that if you measured the circumference of a tree in centimetres, it gives roughly the tree’s age in years. I used the dog’s lead to try it out – although I had to estimate the length of the lead. I got the answer that the silver birch is 25 years old and the oak a hundred years. The oak was quite big, so maybe 100 years is about right. On the way back I met Pat, my next-door neighbour, who remarked that it’s getting lighter in the evenings now. It’s funny how in the spring the days do seem to lengthen rapidly. Of course, it’s the other way round in the autumn: the days shorten rapidly. But in June and December, there seems to be very little variation in the length of the days. I wonder how exactly the length of the day does vary throughout the year. Phew! A busy Monday. I went to the supermarket on the way home from work. Decided to buy some things to make a cauliflower cheese. Funny things cauliflowers. Each little floret (caulifloret?!) looks just like a little cauliflower. And a piece of the floret looks like an even smaller cauliflower. I suppose I could keep on going with this idea for ever, in theory. When part of something looks like the whole thing but on a smaller scale, it’s called ‘self-similarity’ – and that’s something to do with fractals, I think. Perhaps cauliflower cheese should be called ‘fractal cheese’. Tuesday. I glanced through the paper this morning – had at least half a dozen graphs and charts in it relating to various news stories. How the Prime Minster’s popularity has waned compared with that of the Leader of the Opposition. A comparison of inflation rates and interest rates over the last 20 years. Unemployment figures. Even isobars on the weather chart. I wonder how fairly and accurately represented much of the data we get in the newspapers and on TV really is. How true is the phrase ‘lies, damned lies, and statistics’? Watched the evening news on Wednesday. More discussion about the consequences of increasing the size of the European Union. Apparently, the aim is for at least 22 member nations – which would mean a lot of different languages. I suppose it’s not really surprising that a third of all the EU employees in Brussels are translators! Think of all the different translators you’d need. English to French – and French to English. French to Dutch and vice versa. Dutch to German, to Italian, and to Spanish … Mind you, at least some member nations use the same language for EU purposes. I think the total number of different languages is only ten. So what happens when a new nation, with a new language, joins? It’d add another language. But how many more translators? Think I’d need to draw a diagram to get my head round this. Thursday already! Decided I really must pay my enormous phone bill. When I rang Molly later in Vancouver, she told me about a friend being sent a telephone bill for 32 300 dollars instead of 32 dollars 30. Wonder how long I could talk to Molly for 32 000 dollars continuously? It’s hard enough anyway trying to work out when it’s best to call her – Vancouver’s eight hours behind the UK. And when I went to see her last year, as we flew over the different places I found myself wondering what the ‘real’ time was – on the ground – in Greenland and Baffin Bay. Is there a map somewhere showing the different time zones around the world? Friday. It’s Saturday again tomorrow. Sitting at my desk today, trying to write a letter, I found myself distracted by the OU logo. It’s a very simple design really – just a square, a semicircle and a circle. But it’s not really that straightforward. The relative sizes of the three shapes create the overall effect – which is somehow pleasing to the eye. I suppose this is deliberate. I wonder if the logo would look less satisfying if the relative sizes of the shapes were different? There was a thunderstorm in the afternoon – then brilliant sunshine and a rainbow. Why do rainbows happen? Had a discussion with Mike about rainbows, and what the raindrops do to the sunlight to make the colours. We decided between us that reflection of the sun’s rays came into it somehow. But what happens to the light? I know what happens with reflections in a flat mirror, but raindrops aren’t flat. I wonder if it’s the shape of the drops that produces the different colours of the rainbow – or what? Thinking back over this week, there’s been mathematics of some kind everywhere I look. I suppose if you start to think of it like that, maths is just part of everyday life.
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Mathematical musings
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Activity 11

Click on the link above to hear the audio clip called ‘Mathematical musings’.

The speaker describes a number of everyday things and occurrences which she sees as having interesting mathematical features. Make a note of the subjects described and any questions that interest you. Which elements mentioned do you find easy to see as mathematical and which are harder to see that way?

Answer

Below is a list of the topics referred to in the audio clip.

Saturday: Guitar frets, think-of-a-number games, clock arithmetic.
Sunday: Formula for the age of a tree, daylight length.
Monday: Cauliflorets (self similarity*).
Tuesday: Graphs in a newspaper.
Wednesday: How many translators?
Thursday: Phone bill, Time zones, Types of maps.
Friday: OU Logo, rainbows.

Over the coming week, try to cultivate your own ‘mathematical eye and ear’, looking out for ways in which mathematics permeates the various things you do, see and hear.

So, what is mathematics? And what is a mathematician? An aim of this course was to help you begin to answer these questions. However, as you gain more experience of doing mathematics, your own understanding of the words will probably change. So press on with your studies and see how your understanding develops.

Outcomes

Now that you have completed your work on this section, you should have:

  • clarified your own ideas of what mathematics is and what it is to be a mathematician (Activities 1–5, 10 and 11);

  • gained experience in working from videotape and audiotape as part of your mathematical learning (Activities 4 and 11);

  • begun to recognize different types of written mathematics (Activities 6–9);

  • developed your skill at reading mathematics (Activity 9);

  • become more attuned to noticing mathematical questions arising from the world around you (Activities 3, 4, 10 and 11).

MU120_1

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