Posted in ask uncle colin.

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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Posted in ask uncle colin.

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

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Posted in ask uncle colin.

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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Posted in ask uncle colin.

Dear Uncle Colin, I keep being told my work needs to be tidier, but I'm not really sure how to go about that. Do you have any suggestions? - My Exercises Skew Scruffy Hello, MESS, and thanks for your message. I totally feel your pain. In honesty, this is like

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Posted in ask uncle colin.

Dear Uncle Colin, Does the Law Of Large Numbers contradict the fact that the Gambler's Fallacy is a fallacy? - Got A Monkey Backing Liverpool In November's Games Hi, GAMBLING, and thanks for your message! The short answer is: no. I imagine you want a bit more detail than that,

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Posted in ask uncle colin, trigonometry.

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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Posted in ask uncle colin, sport.

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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Posted in ask uncle colin.

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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Posted in ask uncle colin, integration.

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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Posted in ask uncle colin.

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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