# January, 2018

## Ask Uncle Colin: A Plane-teaser

Dear Uncle Colin, In a recent contest, I was told that $a$, $b$ and $c$ were real numbers such that $a-7b+8c=4$ and $8a + 4b -c = 7$. I had to find $a^2 – b^2 + c^2$ and couldn’t see a way in. Can you? – Puzzle Lacks Answer –

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## An “Impossible” New Zealand exam: Part I

To-may-to / tomato; potato / po-tah-to; impossible exam / underprepared students. This time it’s the hapless Kiwis who are making Downfall parody videos and complaining that their practice papers hadn’t prepared them for stuff on the syllabus. Never mind; the formidable @solvemymaths has picked out the two most-complained-about questions, and

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## Ask Uncle Colin: Horizontal Asymptotes

Dear Uncle Colin, I’m working on finding horizontal asymptotes for rational functions. I normally do that by division, but my teacher wants me to do it by rearranging – and I don’t really know what’s going on there! Can you explain? – Horizontal Asymptotes Leaving Me Outwitted Somehow Hi, HALMOS,

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## The Mathematical Ninja and $\sin(15º)$

The Mathematical Ninja sniffed. “$4\sin(15º)$? Degrees? In my classroom?” “Uh uh sorry, sensei, I mean $4\sin\br{\piby{12}}$, obviously, I was just reading from the textmmmff.” “Don’t eat it all at once. Now, $4\sin\br{\piby{12}}$ is an interesting one. You know all about Ailes’ Rectangle, of course, so you know that $\sin\br{\piby{12}}=\frac{\sqrt{6}-\sqrt{2}}{4}$, which

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## Ask Uncle Colin: A mental quotient

Dear Uncle Colin, I have to work out $851 \div 37$ without pen, paper or calculator. How would you do it? – Simple Mental Arithmetic Looks Easy Hi, SMALE, and thanks for your message! I have three ways to tackle it. Brute force and estimation It’s fairly obvious that the

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## Wrong, But Useful: Episode 52

In this month’s episode of Wrong, But Useful, we are joined by maths communication superhero @stecks, who is Katie Steckles in real life. We discuss: Katie’s numerous and various activities as a maths freelancer, including maths busking and being a mathematician-in-residence at the Stephen Lawrence Gallery at the University of

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A question that frequently comes up in the insalubrious sort of place a mathematician might hang around is, what is that value of $0^0$. We generally sigh and answer that the same way every time. It was nice, then, to see someone ask a more fundamental one: what is $0 Read More ## Ask Uncle Colin: A surprising order Dear Uncle Colin, How come$0.3^{0.3} > 0.4^{0.4}$? – Puzzling Over It, Some Surprisingly Ordered Numbers Hi, POISSON, and thank you for your message! It is a bit surprising, isn’t it? You would expect$x^x$to increase everywhere, at first glance. Why it doesn’t We can see that this isn’t Read More ## The Maths Behind… Cakes “Cooking,” said my friend Liz in a recent Facebook post, “is one of the activities where maths is most useful in my everyday life.” She added this picture: I’ve got several reasons for wanting to share this. 1. It’s pretty much a model answer Imagine you’re in a GCSE exam, Read More ## Ask Uncle Colin: Solve this! Dear Uncle Colin, I need to find the largest solution to$e^x + \sin(x)=0\$ and I don’t really know where to start. Any ideas? – Some Options Look Virtually Equal Hi, SOLVE, and thanks for your message! That is something we in the trade call ‘not a very nice equation

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##### Where do you teach?

I teach in my home in Abbotsbury Road, Weymouth.

It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby.