Posted in ask uncle colin.

Dear Uncle Colin, Help! I’m working on a top-secret project somewhere in Buckinghamshire. I can tell you that it involves… components. The… machine has three slots for components, and there are five different components available (one of each) - so there are 60 ways to arrange the components. There’s a

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Posted in logarithms.

I love a good logarithm. Logarithms are a standby for when I want to work something out ninja-style, and there’s something very satisfying about taking something horrible in the powers, bringing it down to the working line, and finding that it wasn’t so horrible after all. I’m an old hand,

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Posted in ask uncle colin.

Dear Uncle Colin, How do I solve $\sin(3x) = \sin(5x)$ for $0 \le x \lt 360$? Seems I Need Extra Smarts Hi, SINES, and thanks for your message! This involves a formula I always have to look up, or work out from scratch. Today I am in a working out

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Posted in dome.

After the Second World War, there was a boom in the study of transmitting encoded data. In likelihood, I imagine the boom started earlier, and the boom was more about the declassified publication of papers on this topic than about a sudden increase in productivity. This month’s mathematical hero, Jessie

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Posted in ask uncle colin.

Dear Uncle Colin, I have a question I can’t make sense of: “It takes 3 bricklayers four hours to lay 4200 bricks. How long would it take 2 bricklayers to lay 3150 bricks?” I can never figure out when to multiply and when to divide! Markscheme Obtusely Recommends Taking A

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Posted in ninja maths.

A physicist. A calculator. The Mathematical Ninja’s face - what could be seen of it - was more snarl than feature. It’s quite tricky to hiss something that doesn’t have any sibilant consonants, but they hissed all the same: “The cube root of 13? You don’t need a calculator for

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Posted in ask uncle colin.

Dear Uncle Colin, I know you don't ask for any money for your incessant blogging, and I've already bought Cracking Mathematics and The Maths Behind - how can I possibly repay you for your work? - Charities Helping Resist Inequality, Serving To Massively Ameliorate Society Hi, CHRISTMAS, and thanks for

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Posted in statistics.

I realised today I’ve been advising my students… not wrong, exactly, but imprecisely. Capriciously. Unmathematically. Even through it was in statistics, where such things are usually tolerated, I felt it was worth putting it right. It was in a scenario such as this: The times an athlete takes to run

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Posted in ask uncle colin.

Dear Uncle Colin, I’m told that $\frac{16^p \times 8^q}{4^{p+q}}=2^n$, and I need to find $n$ in terms of $p$ and $q$. How would I do that? $q$ Uppishly In $n$ Equation Hi, $q$UI$n$E1, and thanks for your message! There are several ways to approach this, as per always. Let’s start

Read More →A puzzle from @Barney_MT: Find angle BDC This turns out to be a bit more demanding than I expected. There are spoilers below the line, showing a solution that took rather more time and space than the final polished version does. Spoilers below the line! Adding in circles When I’ve

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