Posted in ranting

In the olden days, I had a proper job1 writing software for customer survey forms. Among other things, our users could ask their customers to rate how likely it was that they would recommend the product to their friends. Typically, this would be on a ten-point scale, from extremely unlikely

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Posted in ask uncle colin

Dear Uncle Colin, When I'm 8 metres away from a flagpole, the angle of elevation to its top is exactly 40º, according to this angle-measurey-majigger I have here. What will it be when I'm only five metres away? The Hypotenuse Eludes One; Does One Look Into Trigonometric Expressions? Hi, THEODOLITE,

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Posted in podcasts

In Episode 59 of Wrong, But Useful, we’re joined by @el_timbre, who is Emma Bell in real life. We discuss: Emma’s Roots column in Chalkdust1 Number of the podcast: 64, because it’s pleasing, and Dave sings the 64 Zoo Lane theme, which is less so. Emma’s hexastix construction and the

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Posted in Uncategorized

I recently had a flurry of correspondence with translators of The Maths Behind (available wherever etc., but also soon in Swedish and Korean): embarrassingly, they had caught several mistakes in the book. These things happen; we try to put them right and move on. However, it got me wondering: can

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Posted in ask uncle colin, proof, trigonometry

Dear Uncle Colin, I have a trig identity I can't prove! I have to show that $\frac{\cos(x)}{1-\sin(x)} = \tan(x) + \sec(x)$. Strangely Excited Comment About Non-Euclidean Trigonometry. Hi, SECANT, and thanks for your message! This is a slightly sneaky one, but definitely a good one to practice. Let's do it

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Posted in complex numbers

You know how I often bang on about how 'impossible' exams are really nothing of the sort? Well, just for a change, I'm going to bang on about how sometimes exam boards get it wrong. I'm looking at the 2014 Edexcel FP2 paper (the normal one, not the (R) one

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Posted in ask uncle colin, trigonometry

Dear Uncle Colin, I was asked to work out $\tan\br{\theta + \piby 2}$, but the formula failed because $\tan\br{\piby 2}$ is undefined. Is there another way? - Lost Inna Mess, Infinite Trigonometry Hi, LIMIT, and thanks for your message! In fact, there are several ways to approach it! Basic geometry

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Posted in arithmetic, puzzles

An excellent puzzle I heard from @panlepan (I paraphrase, as I've lost the tweet): When you move the final digit of 142857 to the front, you get 714285, which is five times as large. What is the smallest positive integer that is doubled when the last digit moves to the

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Posted in vectors

Dear Uncle Colin, Apparently, the volume of a tetrahedron with three edges given by the vectors $\vec{AB}$, $\vec{AC}$ and $\vec{AD}$, is $\frac{1}{6} \left| \vec{AB} \cdot \br{\vec{AC}\times\vec{AD}} \right|$. Where does that come from? - Very Obviously Lacklustre Understanding of My Exam Hi, VOLUME, and thanks for your message! I think there

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Posted in probability

A nice prompt from @shahlock, some time ago: Math Prompt #apstats #mtbosTwo players A, B. A is 4-0 against B. How would you estimate probability A wins next match? Assume independence — M Shah (@shahlock) November 27, 2016 Stand back, everyone: I'm going to apply Bayes's Theorem. A prior Let's

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