September, 2015

Ask Uncle Colin: how do you find the intersection of three circles?

Dear Uncle Colin, I’ve been challenged to find the area of the intersection of three circles while drawing a Venn diagram. I don’t know where to start!— Triangle Unpredictably Rounded; I’m No Genius For a moment, TURING, I thought there wasn’t a problem in this problem, but then I realised:

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The Mathematical Ninja and the Powers of 10

“So that works out to be $10^{1.6}$,” said the student, reaching for the calculator — and, of course, recoiling as the Mathematical Ninja yelled “yeeha!” and lasso-ed it out of her hand. “Forty,” he said. “Too high by half a percent or so. 39.8.” The student paused. She would normally

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Ask Uncle Colin: Are the log laws… lacking?

Dear Uncle Colin, I have an equation to solve: $\ln(x^2) = 2 \ln(4)\, x \ne 0$. I tried to solve it by applying the log laws: $2 \ln(x) = 2 \ln(4)$, so $x=4$. However, a bit of thought shows that $x=-4$ is also a solution — but that doesn’t seem

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There’s More Than One Way To Do It: Differential Equations

Until fairly recently, I had always done the kind of differential equations you see in Core 4 the same way: separate, integrate, substitute, celebrate. I have taught any number of students the dance; many of them have boogie-woogied their way into a correct answer in exams. But there’s a variation

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Ask Uncle Colin: Multiple workers

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions — and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can. Dear Uncle Colin, I have a problem I just can’t

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How the Mathematical Ninja multiplies by 67

A few months ago, @preshtalwalkar at Mind Your Decisions showed off how he’d advise someone to work out $43 \times 67$ using one of my favourite tricks, the difference of two squares. In fact, that’s how I’d have approached the question at first, too: the two numbers are 12 either

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Ask Uncle Colin: simplifying fractions

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions — and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can. Dear Uncle Colin, I’m having trouble cancelling fractions — in

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The inverse square law

The estimable Barney Maunder-Taylor asked at MathsJam: How come the inverse square law leads to elliptical orbits and equal area swept in equal time? I only know the answer to one of those questions. The differential equations for the inverse square laws work out to be: $\diffn{2}{r}{t} – r \left

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Ask Uncle Colin: A nasty triangle

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions — and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can. Dear Uncle Colin, I’ve been given a trigonometry problem I

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I teach in my home in Abbotsbury Road, Weymouth.

It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby.

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