Posted in geometry.

Since it's Christmas (more or less), let's treat ourselves to a colourful @solvemymaths puzzle: Have a go, if you'd like to! Below the line will be spoilers. Consistency The first and most obvious thing to ask is, is Ed's claim reasonable? At a glance, yes, it makes sense: there's a

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Posted in ask uncle colin.

Dear Uncle Colin, How do I verify the identity $\frac{\cos(\theta)}{1 - \sin(\theta)} \equiv \tan(\theta) + \sec(\theta)$ for $\cos(\theta) \ne 0$? - Struggles Expressing Cosines As Nice Tangents Hi, SECANT, and thanks for your message! The key questions for just about any trigonometry proof are "what's ugly?" and "how can I

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Posted in reviews.

Midway through the second half of You Can’t Polish A Nerd, Steve Mould neatly encapsulates the show in one line: “It creates images on your oscilloscope. It’s so cool!” Because of course you have an oscilloscope. And of course you would use it - or failing that, a balloon and

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Posted in ask uncle colin.

Dear Uncle Colin, How would you factorise $63x^2 + 32x - 63$? I tried the method where you multiply $a$ and $c$ (it gives you -3969) - but I'm not sure how to find factors of that that sum to 32! Factors Are Troublesomely Oversized, Urgh Hi, FATOU, and thanks

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Posted in podcasts.

In this month’s episode of Wrong, But Useful, we’re joined by @ch_nira, who is Dr Nira Chamberlain in real life - and the World’s Most Interesting Mathematician. Nira is a professional mathematical modeller, president-designate of the IMA, and a visiting fellow at Loughborough university. We discuss Nira’s entry in the

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Posted in probability.

I don't remember doing it - although I'd meant to for some time - but apparently I signed up for the British Bone Marrow Registry. (If you're between 17 and 40, you can sign up the next time you give blood; the more people on the register, the more likely

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Posted in ask uncle colin.

Dear Uncle Colin, I have to show that \(-\frac{x}{2} = \ln (\sqrt{1+e^x} - \sqrt{e^x }) + \ln (\sqrt{1+e^{-x}} + 1)\). I can't get it anywhere near the right form! - Proof Of It Not Coming - Any Reasonable Explanation? Hi, POINCARE, and thanks for your message! That's a bit of

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Posted in basic maths skills.

"Three teas, please," said the passenger ahead of me in the queue. The Armorique was due in Plymouth any minute, and tea was of the essence. "That's £4.65, or €5.601." Hang on a moment, I thought, remembering to order my own tea as well. 560 isn't a multiple of 3.

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Posted in game theory.

An emergency blog post about chess, of which I know nothing. This is not meant as serious analysis; think of it more as “here are some topical maths ideas you can throw at your classes.” So, I looked up the Elo ratings for the chess world championship players: in rapid

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Posted in ask uncle colin.

Dear Uncle Colin, I'm told that \(x\sqrt{x} - 5\sqrt{x} = 2\) and I have to find \(x - 2\sqrt{x}\). Everything I try seems to make it worse! Any ideas? Mastering A Cubic - Help Is Needed Hi, MACHIN, and thanks for your message! At first glance, that's a strange one.

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