Another foray into Facebook Maths

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After the success of my last problem-posed-on-facebook, I decided it might be fun to post some more maths for my friends, so on Tuesday afternoon I updated my status:

Alison would love to share some maths with you this afternoon – do you want number patterns or shape?

Well the bad news is that the first couple of responses were very negative – despite the friendliness of my language, and the offer to share some maths rather than impose it on people, led them to post things such as “eeek”, and a sentiment that they wished to run away and hide, with the follow-up comment “Maths is seriously Not Fun”.  This is from people I respect greatly and who I know to be intelligent, articulate, witty individuals, and I dread to think what their experience of maths at school must have been for them to feel such distaste for my favourite subject.

Luckily for my self-esteem, another old friend came along and requested a shape problem, so I posted the following:

You’ll need a ruler, something to write with, and something to write on. Got them? Great, let’s get started!

Draw a triangle. Any triangle you like, as long as it has three straight sides I don’t really mind. Now find the middle of each side, and mark it with a dot. If you wanted to be really clever, you could find the midpoint using a straight-edge and compasses the way the Greeks did, but if you’d rather just measure with the ruler (or even fold your triangle) I won’t mind.

Once you’ve found all three mid-points, join them together: this should split your original triangle into four smaller triangles. Do you notice anything interesting about the smaller triangles?

What happens if you try joining the midpoints of each side of a quadrilateral (four-sided shape)?

And sure enough, a few people rose to the challenge, and started sharing their ideas. One commented several times, first explaining that he’d found it split the original triangle into four that weren’t necessarily the same size or shape, and then coming back to say he always ended up with four congruent triangles, all similar to the original.

Another commenter used vectors to prove the conjecture about joining the midpoints giving congruent triangles with sides half the length of the original, and went on to think about quadrilaterals. His first comment suggested that repeating the process might get you to a smaller version of the original quadrilateral, but he sent me a delighted message later on to say he’d experimented and found he always ended up with parallelograms, and that he’d proved it using his result for triangles.

Someone else saw the triangle problem in a very visual way – he could convince himself very easily what would happen with an equilateral triangle, and then just imagined all other triangles as being transformed, or viewed from a different angle. Some of my facebook friends are easily as imaginitive and happy to explore as the classes I’ve worked with in schools.

There have been plenty of comments along the lines of “Keep them coming” to the maths I’ve posted, which heartens me, but I know that my friends on facebook are not representative of the population as a whole – many are people I studied maths with, or who share an interest in technology and geekery.  I’m glad that each time I do this, some people I wouldn’t necessarily expect to respond are willing to dive in and have a go, and share their insights which are every bit as valuable as the fully and carefully constructed mathematical proofs that others send, but the real challenge will be to engage some of the doubters and maths-phobes, and convince them that actually, Maths is Seriously Fun!

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2 Responses to “Another foray into Facebook Maths”

  1. jspiggott Says:

    It is interesting to note from what you say Alison, that those who can/want to engage with the problems you pose, talk about the mathematics. But, from what I can see, those who do not give emotional responses. Do you think there might be some merit in everybody talking about how problems make them feel rather in what they can do with it?
    So those who are put off by feelings of (for example) not being in control might realise that everyone has a sense of not being “in control” but some see overcoming that lack of certainty as part of the challenge. Perhaps once the “symptoms” are recognised then situations in different settings where one might take risks may help those less engaged to see that they can behave mathematically, they just had not made the connection?

  2. Alison Says:

    That’s a good idea, Jenny. If people could hear my thought processes and feelings as I tackle maths, they’d realise that they are certainly not alone in feeling a lack of control! This is why sometimes when I’m doing some maths I can’t bear to have anyone speak to me about what I’m doing, because I’m feeling so very insecure until I start to make progress. Of course, persuading mathematicians to talk about their feelings might just reinforce stereotypes about mathematicians not having any feelings!

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