The Flying Colours Maths Blog: Latest posts

Ask Uncle Colin: Some Ugly Trigonometry

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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Review: Festival of the Spoken Nerd, You Can’t Polish A Nerd

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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Ask Uncle Colin: A factorising trick

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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Wrong, But Useful: Episode 62

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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Bone Marrow Odds

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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Ask Uncle Colin: A Mess of Logs

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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Exchange rates on board

“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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Maths, Magnus Carlsen, and Making Decisions

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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Ask Uncle Colin: A Cubic That Won’t Come Good

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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All The Maths Podcasts

Since @reflectivemaths wasn’t at Big MathsJam and @samuelhansen was, the MathsJam Special is a bit different this year.

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