Author: Colin

Ask Uncle Colin: 10,958

Dear Uncle Colin, There is a famous puzzle where you're asked to form 100 by inserting basic mathematical operations at strategic points in the string of digits 123456789. This can be achieved, for example, by writing $1 + 2 + 3 - 4 + 5 + 6 + 78 +

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Wrong, But Useful: Episode 42

On this month's episode of Wrong, But Useful, @icecolbeveridge and @reflectivemaths are joined by special guest co-host @christianp. This time, we talk about: Christian, who is involved in @mathsjam and the @aperiodical, and has a number of the podcast: 13. He dislikes it because of its times table; I like

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A Digital Root Puzzle

Every so often, a puzzle comes along and is just right for its time. Not so hard that you waste hours on it, but not so easy that it pops out straight away. I heard this from Simon at Big MathsJam last year and thought it'd be a good one

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Ask Uncle Colin: another vile limit

Dear Uncle Colin, Apparently, you can use L'Hôpital's rule to find the limit of $\left(\tan(x)\right)^x$ as $x$ goes to 0 - but I can't see how! - Fractions Required, Example Given Excepted Hi, FREGE, and thanks for your question! As it stands, you can't use L'Hôpital - but you can

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Ask Uncle Colin: Are normals… normal?

Dear Uncle Colin, I don't understand why the normal gradient is the negative reciprocal of the tangent gradient. What's the logic there? -- Pythagoras Is Blinding You To What's Obvious Hi, PIBYTWO, and thanks for your message! My favourite way to think about perpendicular gradients is to imagine a line

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From Euclid to Cantor

One of my favourite quotes is from Stefan Banach: "A good mathematician sees analogies between theorems. A great mathematician sees analogies between analogies." This post is clearly in the former camp. I'm fairly sure it's a trivial thing, but it's not something I'd noticed before. One of the first serious

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Ask Uncle Colin: Trigonometric inverses and picking the correct quadrant

Dear Uncle Colin, When I have an angle in the second quadrant, I can find it just fine using $\cos^{-1}$ - but using $\sin^{-1}$ or $\tan^{-1}$ gives me an angle in the fourth quadrant. I don't understand why this is! -- I Need Verbose Explanations; Radians Seem Excellent Hi, INVERSE,

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A surprising overlap

Every so often, my muggle side and mathematical side conflict, and this clip from @marksettle shows one of them. My toddler's train track is freaking me out right now. What is going on here?! pic.twitter.com/9o8bVWF5KO — marc blank-settle (@MarcSettle) April 6, 2016 My muggle side says "wait, what, how can

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Ask Uncle Colin: Perpendicular vectors

Dear Uncle Colin, I'm struggling a bit with my C4 vectors. Most of it is fine, except when I have to find a point $P$ on a given line such that $\vec{AP}$ is perpendicular to the line, for some known $A$. How do I figure that out? -- Any Vector

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Wrong, But Useful: Episode 41

This month on Wrong, But Useful, @reflectivemaths and @icecolbeveridge are joined by @evelynjlamb, who is Evelyn Lamb in real life. She writes the Roots Of Unity column for Scientific American. We discuss: How Evelyn got into maths, into writing and into France Evelyn picks the numbers of the podcast: 339,613

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