Posted in dome

Today’s entry in the Dictionary of Mathematical Eponymy is, by some distance, the entry that’s been most useful to me since I learned about it. (The Elo rating is probably in second place.) It’s also a unique entry in that I have next to no information about its originator. What

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Posted in podcasts

In this episode of Wrong, But Useful, we’re joined by @dr_teeluck, who is Dr Vijay Teeluck in real life. We discuss: sunrise (posts by @colinthemathmo and by me got the same answer, someone else disagrees, nice thing to explore) favourite numbers a lovely post by @samhartburn about tetrahedra fitting through

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Posted in ask uncle colin

Dear Uncle Colin, I got stuck trying to prove that $(\sec(x) - \tan(x))^2 \equiv \frac{1-\sin(x)}{1+\sin(x)}$. Can you help? - Bringing Over Is No Good! Bringing Over Is No Good! Hi, BOINGBOING, and thank you for your message! Here’s how I’d tackle it, starting from the left hand side: $\sec(x) -

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Posted in geometry

On Twitter, @Trianglemanscd posed a pertinent problem: Making pizzas tonight but cannot recall how to cut them in 10 slices. — Christopher Danielson (@Trianglemancsd) May 31, 2019 Stand back everyone! I have compasses and a straight-edge and I’m not afraid to use them; the Geogebra demonstration below shows one way

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Posted in ask uncle colin

Dear Uncle Colin, I have twelve coins, one of which is counterfeit. I don’t know if it’s heavier or lighter than the others, but I’m allowed three goes on a balance scale to determine which coin it is and whether it’s light or heavy. Can you help? Some Coins Are

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Posted in algebra

Some time ago, I was surprised to see the following question in a predicted GCSE paper: Solve for $x$: $ \frac{2x}{3x+2} \leq \frac{3}{4x+1}$ Give your answers to two decimal places (3 marks) Why surprised? Surprised because the techniques you need to solve it correctly are Further Maths A-level, rather than

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Posted in ask uncle colin

Dear Uncle Colin, The question says "Under what circumstances does $|\mathbf{a} + \mathbf{b} | = | \mathbf{a} | + | \mathbf{b} |$ and I don’t have a clue. Can you help? Sines? Cosines? Angle Leaves A Residue Hi, SCALAR, and thanks for your message! I have several ways to approach

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Posted in proof

A question that comes up a lot in class is, “how do you get good at proofs?” (It’s usually framed as “I don’t like proofs”, but we’re not having any of that negativity here, thank you very much.) I don’t have a silver bullet for that. I do have some

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Posted in ask uncle colin

Dear Uncle Colin I have the set-up below - how do I find the cumulative density function for $d^2$? - Circles Don’t Fit Hi, CDF, and thanks for your message! Before I start, I’m going to make two simplifying assumptions that don’t change anything1 - that the radius of the

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Posted in dome

We’ve just reached the halfway point of the Dictionary of Mathematical Eponymy project, and it’s time for a fairly famous one (and again, one I’ve been meaning to understand better). What is Noether’s Theorem? Emmy Noether has several theorems named for her, but the first (and probably most important) can

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