# October, 2018

## Ask Uncle Colin: A Set Square Mark

Dear Uncle Colin I just bought a new set square and noticed it had a couple of extra marks - one at seven degrees and one at 42 degrees. Have you any idea what those are for? - Don't Recognise Extra Information Engraved on Calculus Kit Hi, DREIECK, and thank

## A tasty puzzle

Normally when I call something a tasty puzzle, it's a lame local-paper pun about it being to do with cakes or something. In this case, it's not even that. Sorry to disappoint. Instead, it's a puzzle that came to me via reddit: Find $\sum_{i=1}^{10} \frac{2}{4^{\frac{i}{11}}+2}$. Eleventh roots? That's likely to

## Ask Uncle Colin: Platonic Solids

Dear Uncle Colin, Why are there only five platonic solids? - Pentagons Look Awful. Try Octagons! Hi, PLATO, and thanks for your message! A platonic solid is a three-dimensional shape with the following rules: Each face is the same regular polygon The same number of edges meet at every vertex

## Wrong, But Useful: Episode 61

In this month’s episode of Wrong, But Useful, we’re joined by @mscroggs, one of the editors of @chalkdustmag1. Colin has a bug and an article in Chalkdust Matt gives some insights into the editing process at the magazine Number of the podcast: 8 Black History Month: Matt refers to Episode

## Mathematical Dingbats

When I was growing up, we had a game called Dingbats - it would offer a sort of graphical cryptic clue to a phrase and you'd have to figure out what the phrase was. For example: West Ham 4-1 Leicester City Chelsea 4-1 Man Utd Liverpool 4-1 Man City Everton

## Ask Uncle Colin: Some number theory

Dear Uncle Colin, I need to show that $\sqrt{7}$ is in $\mathbb{Q}[\sqrt{2}+\sqrt{3}+\sqrt{7}]$ and I don't really know where to start. We Haven't Approached Tackling Such Questions Hi, WHATSQ, and thanks for your message! I am absolutely not a number theorist, although I must admit to getting a bit curious about

## A moment of neatness

Working through an FP2 question on telescoping sums (one of my favourite topics - although FP2 is full of those), we determined that $r^2 = \frac{\br{2r+1}^3-\br{2r-1}^3-2}{24}$. Adding these up for $r=1$ to $r=n$ gave the fairly neat result that $24\sum_{r=1}^{n} r^2 = \br{2n+1}^3 - 1 - 2n$. Now, there are

Dear Uncle Colin, I'm ok with my basic power laws, but I don't understand why $x^0$ is always 1, and I get mixed up when it's a fraction or a negative power. Can you help? Running Out Of Time Hi, ROOT, and thanks for your message! If it's any consolation,

## Ten great books to give an interested mathematician

Oh no! Your favourite mathematician has a birthday/Christmas/other present-giving occasion coming up and you don't know what book to get them! They've already got Cracking Mathematics and The Maths Behind, obviously... so what can you give them this year? Fear not, dear reader. I am at hand to list some

## Ask Uncle Colin: Some Rigour Required

Integration by substitution, rigorously Dear Uncle Colin, Can you explain why integration by substitution works? I get that you're not allowed to 'cancel' the $dx$s, but can't see how it works otherwise. - Reasonable Interpretation Got Our Understanding Ridiculed Hi, RIGOUR, and thanks for your message. First up, confession time: