The Flying Colours Maths Blog: Latest posts

Ask Uncle Colin: a load of balls

Dear Uncle Colin, I struggled with a problem where you had 5 blue balls and x green balls, and the probability of picking two blue balls out of the bag was $\frac{5}{14}$. I can’t really see where to start! -Baffled About Likelihood, Lacking Startpoint Hi, BALLS, thanks for your message!

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On degrees

I gave a talk (some months ago now) on the history of $\pi$ (which is well discussed in my unreliable history of maths, Cracking Mathematics, available wherever good books are sold.) At one point, I put up a slide generally excoriating degrees as a measurement of angle, and stating that

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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

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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

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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

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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

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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

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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

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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

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Ask Uncle Colin: Powers

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,

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