Posted in ask uncle colin

Dear Uncle Colin, This is the fifth time in the last six World Cups that Nigeria have been drawn against Argentina in the group stages. What are the odds?! – Coincidences At FIFA? Unlikely! Hi, CAFU, and thanks for your message! I’m going to make some simplifying assumptions for this

Read More →In previous articles, I’ve looked at how to find $\cos(72º)$ using some nasty algebra and some comparatively nice geometry. In this one, inspired by @ImMisterAl, I try some nicer – although quite literally complex – geometry. De Moivre’s Theorem I’m going to assume you’re ok with complex numbers. If you’re

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Posted in ask uncle colin, Uncategorized

Dear Uncle Colin I have a percentages problem: I’m told that in an election, 95.74% of the electorate voted for the winning side. What is the minimum possible size of the electorate? – Percentages Often Lack Logic Hi, POLL, and thank you for your message! There are two possible answers

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Posted in podcasts

Owing to a spotty connection, the sound quality is a bit patchy on this one. Apologies. In this month’s installment, we are joined by Belinda Keir. We discuss: Belinda convenes the Sydney MathsJam and is on the committee for the Celebration of Mind What makes a mathematician? Why Belinda is

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Posted in trigonometry

Some months ago, I wrote about a method for finding $\cos(72º)$, or $\cos\br{\frac{2\pi}{5}}$ in proper units. Almost immediately, the good people of Twitter and Facebook – notably @ImMisterAl (Al) and @BuryMathsTutor (Mark)- suggested other ways of doing it. Let’s start with Mark’s method, which he dissects in his book GCSE

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Posted in ask uncle colin

Dear Uncle Colin, I’m trying to solve $3^{2x+1} – 28\times 3^x + 9 =0$. I’ve split up the first term into $3 \times 3^{2x}$ but then I’m stuck! Any suggestions? Likely Overthinking Gettable Sum Hi, LOGS, and thanks for your message! You’ve made a really good start there. The piece

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Posted in integration, trigonometry

The ever-challenging Adam Atkinson, having noticed my attention to the “impossible” New Zealand exams, pointed me at a tricky question from an Italian exam which asked students to verify that, to give a smooth ride on a bike with square wheels (of side length 2), the height of the floor

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Posted in ask uncle colin, vectors

Dear Uncle Colin Do you have any tips for sketching three-dimensional vectors? Every time we have an A-level question, my teacher says “draw a diagram!” but I don’t know how to draw in 3D. – Got A Useless Sketching Situation Hi, GAUSS, and thank you for your message! Three-dimensional vectors

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Posted in arithmetic

That @solvemymaths is an excellent source of puzzles and whathaveyou: Meanwhile, back in 1940 when everything was basically shit… pic.twitter.com/A5eKXOunFC — Ed Southall (@solvemymaths) October 7, 2017 How would you find $\sqrt[3]{\frac{1-x^2}{x}}$ when $x=0.962$, using log tables or otherwise? I would start by trying to make the numbers nicer: I

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Posted in ask uncle colin, ranting

Dear Uncle Colin, I’m sitting my GCSE Maths starting tomorrow. What will the grade boundaries be? – First Exams Are Redoubtable Hi, FEAR, I’m writing this, believe it or not, in early February1. I’m not even sure this summer’s GCSE papers have been written yet, but I am going to

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