# 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 –

## 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

## 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,

## 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

## 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

## 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