March, 2018

Ask Uncle Colin: A Misbehaving Inverse

Dear Uncle Colin, Why is $\arcsin\br{\sin\br{\frac {6}{7}\pi}}$ not $\frac{6}{7}\pi$? – A Reasonable Conclusion Seems Incorrect Numerically Hi, ARCSIN, and thanks for your message! On the face of it, it does seem like a reasonable conclusion: surely feeding the output of $\sin(x)$ into its inverse function should get you back where

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The Stuckness of Andrew Wiles

One of the most famous examples of stuckness – both for maths as a whole and for a mathematician in particular – is Fermat’s Last Theorem, which states that there is no solution to $a^n + b^n = c^n$ for whole numbers $a$, $b$, $c$ and $n$ unless $n$ is

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Ask Uncle Colin: A Fractional Limit

Dear Uncle Colin, I need to find the limit as $x$ approaches 1 of $\frac{x^{29}-1}{x-1}$. I tried factoring out $x^{28}$ but didn’t get anywhere. – Learning How Others Proceed In This Awful Limit Hi, LHOPITAL, and thanks for your message! Factoring out an $x^{28}$ is very unlikely to get you

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Cowboy Completing The Square

Factorising a quadratic? It’s nice when it comes off, but there’s a lot of guesswork, and no guarantee it even factorises. Completing the square? Who has time for all that algebra? And as for the quadratic formula, or your clever calculator methods: honestly, what are you, an engineer? There is

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Ask Uncle Colin: A multi-cubic integral

Dear Uncle Colin, I need to calculate $\int x^3 (x^3+1) (x^3 + 2)^{\frac 13} \dx$ and it’s giving me a headache! Can you help? I’ve Blundered Using Parts, Rolled Out Fourier Expansions… Nothing! Hi, IBUPROFEN, and thanks for your message! That’s a bit of a brute, but it can be

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Wrong, But Useful: Episode 54

In this month’s installment of Wrong, But Useful, Colin and Dave are joined by mathematical editor and proofreader @samhartburn. We apologise for the sound quality. We’ve done the best we can. Sam enjoys @robeastaway‘s Maths On The Go with her primary-school children. Dave plugs Colin’s books. It takes us some

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Another @solvemymaths problem

Another geometry puzzle from @solvemymaths: I enjoyed this one — no solution immediately jumped out at me, and I spend a great deal of time looking smugly at a way over-engineered circle theorems approach I can no longer remember. Let’s label the apex of the triangle P, and the octagons

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Ask Uncle Colin: A Weird Arithmetic Progression

Dear Uncle Colin, I'm told that the three terms $a_1 = \log(2)$, $a_2 = \log(2\sin(x)-1)$ and $a_3 = \log(1-y)$ are in arithmetic progression and I need to find the range of possible values for $y$. I don't really know where to start! – Logarithmic Arithmetic Progression Lacks A Clear Explanation

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A RITANGLE problem

When RITANGLE advises you to use technology to answer a question, you know it’s going to get messy. So, with some trepidation, here goes: (As usual, everything below the line may contain spoilers.) It’s easy enough to do this in Geogebra – but somehow a little bit unsatisfactory to move

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