The Flying Colours Maths Blog: Latest posts

A PSA on Cylinders and Prisms

OK, listen up, there seems to be some confusion about this. I shall make the point several times here, but first I shall make it in bold: Cylinders are not prisms. In fact, it’s the other way around. A cylinder is a 3D shape that has parallel end-faces and a

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Wrong, but Useful: Episode 76b

What's this? Didn't we have a WBU last week? We did indeed. Only we cut out a section of our conversation with @dr_teeluck about APR to keep the episode length (somewhat) reasonable. Here it is as a special bonus episode for your enjoyment.

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Ask Uncle Colin: A Pointy Thing

Dear Uncle Colin, What do you call the ‘point’ of the absolute value graph - for instance, $(0,0)$ on the graph of $y=|x|$? It can’t be a minimum because the gradient is undefined! Proof Or It’s Not True Hi, POINT, and thanks for your message! I hate to go ‘well,

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Dictionary of Mathematical Eponymy: Osborn’s Law

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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Wrong, But Useful: Episode 76

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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Ask Uncle Colin: A Trigonometric Identity

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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A Tenth Of A Pizza

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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Ask Uncle Colin: The Twelve Coin Puzzle

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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A GCSE surprise

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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Ask Uncle Colin: A Pair of Vectors

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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