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 +

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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,

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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

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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

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Posted in ask uncle colin

Dear Uncle Colin, I was asked to complete the square on $f(x) = 2x^2 + 13x + 20$. I started by halving everything, which makes it cleaner, but the solution manual disagrees. What gives? – Have Always Loathed Functions Hi, HALF, and thanks for your message! Dividing a quadratic by

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Posted in podcasts

In this month’s episode of Wrong But Useful (#53), brought to you by the power of Lemsip and a day in bed, Colin and Dave are joined by Special Guest Co-Hosts @sean_jamshidi and #NikiWithoutTwitter, who are Sean Jamshidi and Niki Kalaydzhieva from Chalkdust Magazine1 in real life. Niki is an

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Posted in geometry

“Is Hamburg that much further north than London?” I furrowed my brow. Hamburg, to the best of my knowledge, is not that much further north than London. But here it was, written in stone (on the side of Durlston Castle in Swanage.) (I’ve transcribed the sign at the bottom of

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Posted in ask uncle colin, trigonometry

Dear Uncle Colin, How would you calculate $\cos(72º)$ by hand? – Pointless Historical Inquiry Hi, PHI, and thanks for your message. There seems to be an awful lot of degree use around at the moment, and I’m not very happy about it. But still, in the spirit of answering what

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Posted in quadratics

Last time, we looked at an ‘impossible’ question from a New Zealand exam, which was (of course) nothing of the sort. The second question highlighted as a brute was this one: (Full exam is here.) But, you see, I look at that and think… part (iv) isn’t straightforward on its

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Posted in ask uncle colin

Dear Uncle Colin, In a recent contest, I was told that $a$, $b$ and $c$ were real numbers such that $a-7b+8c=4$ and $8a + 4b -c = 7$. I had to find $a^2 – b^2 + c^2$ and couldn’t see a way in. Can you? – Puzzle Lacks Answer –

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