The Flying Colours Maths Blog: Latest posts

Ask Uncle Colin: A peculiar triangle

Dear Uncle Colin, I have a triangle. All I know is that its angles, $\alpha$, $\beta$ and $\gamma$, satisfy $\cos(\alpha)=\frac{1}{4}$ and $\gamma = 30º$ – and I have to find $\tan(\beta)$. Help! – Can't Obviously See It, Need Explanation Hi, COSINE, and thanks for your message! This is one that

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Wrong, But Useful: Episode 51, featuring @suedepom

Sue de Pomerai joins Colin and Dave for this month’s episode of Wrong, But Useful. We discuss: Her work for FMSP and MEI and, previously as a teacher Sue’s alter ego, Ada Lovelace, and getting more young women into maths Colin writes books: he mentions Cracking Mathematics and some good

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The Sneakiest Integral I’ve Ever Done

Once upon a time1, @dragon_dodo asked me to help with: $\int_{- \piby 2}^{\piby 2} \frac{1}{2007^x+1} \frac{\sin^{2008}(x)}{\sin^{2008}(x)+\cos^{2008}(x)} \dx$. Heaven – or the other place – only knows where she got that thing from. Where do you even begin? My usual approach when I don't know where to start is to start

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Ask Uncle Colin: Expected goals

Dear Uncle Colin, What on earth is “expected goals” and why is it supposed to be useful? – Just Enjoy Football FFS Hello, JEFF, and thanks for your message! The first part of your question is simple, although with some subtleties. What does ‘expected goals’ mean? ‘Expected goals’ is a

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An unexpected connection

You want to know one of my favourite things about maths? It's the connections. Connections between things that don't, on the face of it, seem remotely connected. One just cropped up, and made me grin from ear to ear, so I thought I'd share it with you. The Parker Square

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Ask Uncle Colin: Winning the Lottery

Dear Uncle Colin, Can you help me win the lottery using MATHS!? – Lots Of Time, Tremendous Optimism No. I mean, there's a chapter in The Maths Behind1 on exactly that topic, but honestly? If I knew how to win the lottery, I'd be drinking mocktails on a Caribbean beach

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A quadratic simultaneous equation

A charming little puzzle from Brilliant: $x^2 + xy = 20$ $y^2 + xy = 30$ Find $xy$. I like this in part because there are many ways to solve it, and none of them the 'standard' way for dealing with simultaneous equations. You might look at it and say

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Ask Uncle Colin: Evil in integral form

Dear Uncle Colin, I've been set an evil integral: $\int_0^\piby{4} \frac{\sqrt{3}}{2 + \sin(2x)}\d x$. There is a hint to use the substitution $\tan(x) = \frac{1}{2}\left( -1 + \sqrt{3}\tan(\theta)\right)$, but I can't see how that helps in the slightest. — Let's Integrate Everything! Hello, LIE, and thank you for your message!

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Long division

Some time back in the olden days, @robeastaway posted this: My 11 year old's sample SATs papers found in his book bag. "Work out 1118÷43 (no calculator)." I wish all ministers had to take these tests. — Rob Eastaway (@robeastaway) March 22, 2017 Before I say anything else: I

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Ask Uncle Colin: I keep forgetting stuff!

Dear Uncle Colin, I’m revising for a high-stakes exam. I learn material, do the exercises and think I understand it – but when I revisit it a couple of weeks later, it feels like I’m starting from scratch. What can I do to remember things better? — Failure Of Remembering

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