The Flying Colours Maths Blog: Latest posts

The Mathematical Ninja and the twenty-sixths

The Mathematical Ninja played an implausible trick shot, not only removing himself from a cleverly-plotted snooker, but potting a red his student had presumed safe and setting himself up on the black. Again. “One!” he said, brightly, and put some chalk on the end of his cue. The student sighed.

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Wrong, But Useful: Episode 35

In this month’s Wrong, But Useful, Dave and Colin discuss: Colin gets his plug for Cracking Mathematics in early Colin is upset by a missing apostrophe Dave teases us with the number of the podcast and asks about the kinds of things it’s reasonable to expect students to know, and

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Ask Uncle Colin: Simultaneous Equations

Dear Uncle Colin, Could you please tell me how to solve simultaneous equations? I have a rough idea, but I get confused about it. — Stuck In Mathematical Examinations/Qualifications Hello, SIMEQ! Here’s how I attack linear simultaneous equations, such as: $5x + 6y = -34$ (A) $7x + 2y =

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A curious identity

There’s something neat about an identity or result that seems completely unexpected, and this one is an especially nice one: $$ e^{2\pi \sin \left( i \ln(\phi)\right) }= -1$$ (where $\phi$ is the golden ratio.) It’s one of those that just begs, “prove me!” So, here goes! I’d start with the

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Ask Uncle Colin: Trigonometric craziness

Dear Uncle Colin, My friend claims that $\frac { 2 – \frac{2 \sin(x)}{\cos(x)}}{\sin(x) – \cos(x)} \equiv -2\sec(x)$. I think she’s crazy. What do you think? — I Don’t Even Need Trigonometry, I Teach Yoga Hi, IDENTITY — even yoga teachers need trigonometry, though! Well, there’s one way to find out

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How to invert a $3 \times 3$ matrix

So much wasted time. I spent much of my first two years at university cursing the names of Gauss and Jordan, railing at my lecturer (who grim-facedly assured me there were no more useful uses of a student’s thinking time than ham-fistedly rearranging these things), and thinking “there MUST be

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Ask Uncle Colin: I’ve lost my mojo

Dear Uncle Colin, I’m struggling with A-level. I used to love maths when I did [one board] at GCSE and now I’m doing [another board] at A-level, I don’t enjoy it any more — when I see a question, I can’t even tell what it is they’re asking. My teachers

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Review: The QAMA Calculator

It’s billed as the calculator that won’t think until you do: if you give it something to evaluate, it will refuse to give you an answer until you give it an acceptable approximation. On the surface, that’s a great idea. If I had a coffee for every time I’ve rolled

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Ask Uncle Colin: An Undefined Integral

Dear Uncle Colin, I have a disagreement with my teacher about the integral $\int_{-1}^{1} x^{-1} \dx$. I understand you have to split the integral into two parts, which I’m happy with. They split it from -1 to $a$, letting $a \rightarrow 0_-$ and from $b$ to 1, letting $b \rightarrow

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A lovely trigonometric identity

When I was researching the recent Mathematical Ninja piece for Relatively Prime, I stumbled on something at MathWorld1 I’d never noticed before: if $t = \tan(x)$, then: $\tan(2x) = \frac{2t}{1 – t^2}$ $\tan(3x) = \frac{3t – t^3}{1 – 3t^2}$ $\tan(4x) = \frac{4t – 4t^3}{1 – 6t^2 + t^4}$ $\tan(5x) =

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