Posted in quadratics, there's more than one way to do it.

Factorising a quadratic? It’s nice when it comes off, but there’s a lot of guesswork, and no guarantee it even factorises. Completing the square? Who has time for all that algebra? And as for the quadratic formula, or your clever calculator methods: honestly, what are you, an engineer? There is

Read More →
Posted in ask uncle colin, integration.

Dear Uncle Colin, I need to calculate $\int x^3 (x^3+1) (x^3 + 2)^{\frac 13} \dx$ and it’s giving me a headache! Can you help? I’ve Blundered Using Parts, Rolled Out Fourier Expansions… Nothing! Hi, IBUPROFEN, and thanks for your message! That’s a bit of a brute, but it can be

Read More →
Posted in podcasts.

In this month’s installment of Wrong, But Useful, Colin and Dave are joined by mathematical editor and proofreader @samhartburn. We apologise for the sound quality. We’ve done the best we can. Sam enjoys @robeastaway‘s Maths On The Go with her primary-school children. Dave plugs Colin’s books. It takes us some

Read More →
Posted in geometry.

Another geometry puzzle from @solvemymaths: I enjoyed this one — no solution immediately jumped out at me, and I spend a great deal of time looking smugly at a way over-engineered circle theorems approach I can no longer remember. Let’s label the apex of the triangle P, and the octagons

Read More →
Posted in ask uncle colin.

Dear Uncle Colin, I'm told that the three terms $a_1 = \log(2)$, $a_2 = \log(2\sin(x)-1)$ and $a_3 = \log(1-y)$ are in arithmetic progression and I need to find the range of possible values for $y$. I don't really know where to start! – Logarithmic Arithmetic Progression Lacks A Clear Explanation

Read More →When RITANGLE advises you to use technology to answer a question, you know it’s going to get messy. So, with some trepidation, here goes: (As usual, everything below the line may contain spoilers.) It’s easy enough to do this in Geogebra – but somehow a little bit unsatisfactory to move

Read More →
Posted in ask uncle colin, quadratics.

Dear Uncle Colin, I was wondering: given a quadratic function with real coefficients, what complex arguments lead to real answers? – Researching Equations And Lines Hi, REAL, and thanks for your message! This turns out to be simpler than I expected: if you have a quadratic $f(z) = az^2 +

Read More →
Posted in puzzles.

By way of @ajk_44 at NRICH, a belter of a puzzle: You have 27 small cubes – three each of nine distinct colours. Can you arrange them in a cube so that each colour appears once on each face? (Alison has created a Geogebra widget for you to play with,

Read More →
Posted in ask uncle colin.

Dear Uncle Colin, I’m told that a rectangular box has a surface area of 64cm2, and I have to find the maximum possible volume. How would I do that? – Can Uncle Bring Obviousness Into Differentiation? Hi, CUBOID, and thanks for your message – I certainly hope I can! We

Read More →
Posted in dialogue, statistics.

I challenge you to write an interesting blog post about random number tables — Jo Morgan (@mathsjem) June 28, 2017 If you flick to the back of an old A-level formula sheets, you might spot a list of random digits like this one from an MEI book: Why on earth

Read More →