Posted in integration.

An interesting “creative” integral pointed my way by the marvellous @DavidKButlerUoA: Find $\int {\frac{1}{(1+x^2)^2}} \dx$ There are “proper” ways to do this - in his tweet, David shows a clever way to do it by parts, and suggests a trig substitution as an alternative. I want to show a third

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Posted in ask uncle colin.

Dear Uncle Colin, I’m trying to invert $y = \arcsin\br{x^2 + 4x - 5}$, but I get stuck at $x^2 + 4x = \sin(y) + 5$. Any pointers? - All Routine Calculations Should Invert Naturally Hi, ARCSIN, and thanks for your message! Just before I dive into this, I have

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Posted in ranting.

On a recent1 episode of Wrong, But Useful, Dave noted that 33 of the first 100 Fibonacci numbers were even, 333 of the first 1000, and so on. My reaction wasn’t quite as it should have been: I said something like “well, yes, obviously”. While there’s a not-too-difficult reason behind

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Posted in ask uncle colin.

Dear Uncle Colin, I need to work out $\lim_{x\to\infty} \left\{ \left[ \frac{ 2^{1/x} + 8^{1/x} }{2} \right]^x \right\}$. The textbook says it’s four, but my engineering friends all get different answers. How would you work it out? - Giving Engineers Real Maths Analysis Is Naive Hi, GERMAIN, and thanks for

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Posted in ask uncle colin.

Dear Uncle Colin, I’m meant to be sitting my A-levels this summer and there’s an awful disease going around. I don’t know if school will be open next week or even if the exams will go ahead. I don’t know what that means for university. I’m scared. What do I

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Posted in ninja maths.

“The square root of two… I don’t even know how to say this. The square root of two to the square root of threeth power?” “$\sqrt{2}^{\sqrt{3}}$?” said the Mathematical Ninja. “I wouldn’t bother saying it, I’d just write it down.” “But what does it mean? I mean, I can just

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Posted in podcasts.

In this month's Pi Day Special episode, we're joined by @aap03102, who is Chris Smith in real life. We discuss: Negative primes Surdoku (look in issue $2^5$) Chris's dark past Chalkdust book of the year Book (or writing) ideas (I’m trying to compile a big list of maths things I

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Posted in ask uncle colin.

Dear Uncle Colin, I’ve been asked to show how to do $23241 \div 31$ in base 5 by long division - I can barely do it in base 10! Help! - Lots Of Number Games Hi, LONG, and thanks for your message! There are several steps to working a long

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Posted in ranting.

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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Posted in podcasts.

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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