Posted in ask uncle colin

Dear Uncle Colin, I had a question in an exam that gave a cubic, $f(x) = x^3 – 8x^2 + cx + d$, with roots $\alpha$, $\beta$ and $\gamma$. When plotted on an Argand diagram, the triangle formed by the three roots has area 8. Given that $\alpha=2$, find $c$

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Posted in podcasts

In Episode 56 of Wrong, But Useful, we’re joined by @zoelgriffiths (Zoe Griffiths), maths communicator from Think Maths. Zoe had her poem e, to thee, x in @chalkdustmagazine recently, and did a set about misleading statistics at @aeoud (An Evening Of Unnecessary Detail) Bad polls and fake stats, including this

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Posted in reviews

It turns out, I made an error in Cracking Mathematics. Not (in this case) a mathematical or historical error, although there are plenty of those1 but an error of etiquette: my potted biography of John Horton Conway emphasised the Game of Life above the rest of his work; I imagine

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Posted in ask uncle colin

Dear Uncle Colin, I’m practicing for the Oxford PAT and have been asked how many terms of the binomial expansion would be needed to determine $(3.12)^5$ to one decimal place? I don’t really know where to start. – Knows Expansions (Binomial); Lacks Explanations Hi, KEBLE, and thanks for your message!

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Posted in ninja maths, probability

A professor – according to Reddit – asked their class how many people you’d need to have in a room to be absolutely certain two of them would have Social Security numbers1 ending in the same four digits (in the same order). 10001, obviously. How about a probability of 99.9%?

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Posted in ask uncle colin

In this post, I swap liberally between d-notation and ‘-notation for derivatives. Deal with it. Dear Uncle Colin, Why do we have to treat second-order ODEs differently when the auxiliary equation has a repeated root? Something Or Other Defies Expectations Hi, SOODE, and thanks for your message! First, some background

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Posted in matrices

I remember, with a faint feeling of dread, having to calculate the eigenvalues of a matrix. It became routine in the end, but I was recently reminded of the pain when a student asked if there was a shortcut. For a 2-by-2 matrix? Yes. It is up to you, though,

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Posted in algebra, ask uncle colin

Dear Uncle Colin, I was trying to work out $\frac{\frac{3}{7+h}-\frac{3}{7}}{h}$, and I got it down to $\frac{\frac{3}{h}}{h}$ – but that’s not the answer in the book! What have I done wrong? – Likely I’ve Mistreated It Terribly Hi, LIMIT, and thank you for your message! I’m afraid you’re right, you

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Posted in podcasts

This month, it’s Gathering4Gardner special, largely recorded in Atlanta with Adam Atkinson and @dragon_dodo. We discuss: Our favourite talks of the event, including: The Juggler Problem The Taxman Problem Ramanujan Sums Optical illusions Doris Schattschneider’s talk on Marjorie Rice, an amateur mathematician who made huge leaps in the study of

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Posted in algebra

Last time out, I looked at a problem unearthed by @mathsjem – to find the cube root of a degree-six polynomial. This led (unsurprisingly) to a quadratic: $3 + 4x – 2x^2$. When checking whether this was indeed the answer, I hit a problem: is there a simple way to

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