Posted in ask uncle colin, circles, geometry.

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:

Read More →
Posted in logarithms, ninja maths.

“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

Read More →
Posted in ask uncle colin, logarithms.

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

Read More →
Posted in integration.

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

Read More →
Posted in ask uncle colin.

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

Read More →
Posted in ninja maths.

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

Read More →
Posted in ask uncle colin, 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

Read More →
Posted in modelling.

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

Read More →
Posted in ask uncle colin, core 3, trigonometry.

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

Read More →