You don’t need Pythagoras to see if your new fridge will fit

Janet Downs's picture

Children should learn ‘fundamental, abstract mathematics’ such as Pythagoras’s theorem, schools minister Nick Gibb told the Schools Week/FE Week* fringe meeting at the Tory Conference last week. Pythagoras, he explained, could be ‘useful if you are buying a tall fridge in a house that has low ceilings’.

But there’s a much quicker method to solve this thorny problem than doing a calculation based on Pythagoras. You use a tape measure to find the height of the fridge (or check the fridge specifications). You measure up the wall to see how far away the height of the fridge is away from the ceiling. If there’s still space above the end of the tape then your fridge will fit. If you can’t stretch out the tape to the measured height then you’ll need to buy a shorter fridge or put the fridge somewhere else.

Being able to use Pythagoras to solve the fridge space problem doesn’t mean it’s appropriate to do so. Why take a difficult path when there’s an easier one?

Why, then, should children learn Pythagoras? Gibb’s correct that there are practical applications for the theorem. It’s used by architects, builders, electricians, surveyors, map makers, archaeologists, glaziers, engineers… and, of course, mathematicians. But the most important reason is that it’s a problem – and problems are meant to be solved.

The first problem, and the one set by my maths teacher Mrs D over half a century ago, is to find the relationship between the squares on the three sides of a right-angled triangle using a diagram of a right-angled triangle, squared paper, scissors and glue. Present results using mathematical terms. I realise this method might be too progressive for some - it involves pupils discovering things instead of being told. But the lesson stuck (and not just because I was using glue).

Had Mrs D given the lesson today, she might have followed up with a short animation although I think she would have shuddered at the rap.

The second problem, or rather problems, is using Pythagoras (see suggestions here). Mrs D had scores of them which took us right up to O level. You can even laugh at Pythagoras – it’s featured in the Simpsons although Homer has to be corrected. And you can sing the chorus in Danny Kaye’s song.

The point of learning maths, abstract and practical, is that it’s exciting. It isn’t just for checking whether white goods will fit in a confined space (dull, unimaginably dull). And it isn't to climb up PISA's slippery pole. It’s looking for patterns, puzzles, challenges.

In my research for this article I stumbled across Simon Singh talking about ‘The Simpsons and their Mathematical Secrets’. Just a few minutes in and I’m learning about Mersenne primes. Mrs D would have been thrilled. Let’s hope Nick Gibb is similarly enthused.

*See page 12 of supplement downloadable here.


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Leah K Stewart's picture
Mon, 12/10/2015 - 14:33

Thanks for this Janet. You may also like this blog post for a UK maths professor now working in the states: Letter to a calculus student – The Sequel ( I'd love it if people in power who don't care about maths, except in relation to our scores on international tests, would be a little quieter about the reasons to study maths so those who love it can be heard more clearly. Like your Mrs D and like Keith Devlin and many others who are inspiring when they talk about maths.

David Barry's picture
Mon, 12/10/2015 - 16:20

Nick Gibb's proposal, that if you want to work out whether a fridge will fit, one should use trigonmetry (So I presume that you use a theodolite to take a sighting on the top of the fridge, and then take a similar bearing on the ceiling, and after that, equipped with a knowledge of Pythagoras, the calculation ought to be simple ) reminds me of the techniques used by the ruling class on the flying Island of Laputa, as described by Lemuel Gulliver. He describes them thus:-

"Their houses are very ill built, the walls bevil, without one right angle in any apartment; ...... those instructions they give being too refined for the intellects of their workmen, which occasions perpetual mistakes. And although they are dexterous enough upon a piece of paper, in the management of the rule, the pencil, and the divider, yet in the common actions and behavior of life, I have not seen a more clumsy, awkward, and unhandy people, nor so slow and perplexed in their conceptions upon all other subjects, except those of mathematics....... They are very bad reasoners, and vehemently given to opposition, unless when they happen to be of the right opinion, which is seldom their case. Imagination, fancy, and invention, they are wholly strangers to, nor have any words in their language, by which those ideas can be expressed; the whole compass of their thoughts and mind being shut up within the forementioned sciences. "

Jane Eades's picture
Mon, 12/10/2015 - 23:29

There is also the point that it is an introduction to logical argument and proof. This is something which is seriously lacking in many of the arguments put forward by this Government and others commenting on education. "standards have got worse", "classes are out of control", "privatising schools improves results' ..........

Perhaps those who make unfounded generalisations with nothing to support their claim should be forced to write an essay on why Pythagorus's theorem is not a matter of opinion!

Janet Downs's picture
Tue, 13/10/2015 - 06:05

Jane - it's now flooding back. I remember Mrs D was very keen on logic. She would insist every maths calculation was laid out in a particular manner (one line for each stage of the calculation; equal signs under equal signs etc). We had to lay out proofs for every theorem giving each logical step, laid out as above and always, always ending 'QED', 'quod erat demonstrandum' to show we had proved what we set out to prove.
Logic, precision, accuracy were her watchwords. I'm beginning to realise Mrs D had an effect on me that goes beyond mathematics.

Janet Downs's picture
Tue, 13/10/2015 - 06:17

Today is World Maths Day. Let's celebrate!

Jane Eades's picture
Tue, 13/10/2015 - 08:17

I think that, Janet, you had a better teacher than I did. Most of the members of my class learned their theorems off by heart. "I being poor" at memory, "had only my" logic and during exams would often have to work them out from first principles. It should always have been the ability to do that which should have been taught.

I have also demonstrated the randomness of things taught by rote. The quotes above are from GCSE English Lit in 1960, together with "quam quam sunt sub aqua, sunt sub aquat malidiceri (?) tentant(?)" for the "O" level latin I failed hopelessly - goodness only know what it means! There is another from a Rupert Brooke in Greek which I can say but cannot write.

How useless these latter are and how useful the ability to compensate for a poor memory through understanding and an ability to learn, rather than be taught - hence, you, Janet, and I have taught ourselves how to use computers. I have taught myself how to fix electric lights and sockets (being a girl, my education was focussed on cooking and sewing). I have set up websites and a host of other things.

Education policy currently is based on being able to regurgitate information, often with little understanding, is a mark that education has been successful (as well as putting huge amounts of money into the exam boards' pockets).

And now I will just have to get that sum at the bottom right without using a calculator - is it in the times tables?

Janet Downs's picture
Wed, 14/10/2015 - 09:14

Jane - the only Latin I can remember, apart from Amo, Amas, Amat.. is O me miserum (Woe is me) and Vae Tibi (Woe to you). I didn't even get as far as O level but I wish I'd learnt it now as I like a challenge.

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A Cooper's picture
Tue, 13/10/2015 - 08:29

Reminds me of the urban legend: NASA spent millions of dollars developing an an anti-gravity pen in the 1960s. The project was eventually abandoned due to spiralling costs - astronauts just continued to use mechanical pencils.

Janet Downs's picture
Wed, 14/10/2015 - 09:17

Similar to the story about a kid who entered a competition to design a tool for an elderly person who couldn't bend down to pick up a milk bottle from the step. He designed a shelf to stick on the wall so the oldie could reach for the bottle without bending. Low tech but far more appropriate than gadgets for squeezing round slippery milk bottles.

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