Posted in ask uncle colin, binomial, logarithms.

Dear Uncle Colin, I noticed that $2^{\frac{1}{1,000,000}} = 1.000 000 693 147 2$ or so, pretty much exactly $\left(1 + \frac{1}{1,000,000} \ln(2)\right)$. Is that a coincidence? Nice Interesting Numbers; Jarring Acronym Dear NINJA, The easiest way to see that it’s not a coincidence is to check out $3^{\frac{1}{1,000,000}} $, which

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Posted in big in finland, reviews.

It’s genuinely difficult to write an innovative maths book, something that’ll teach even the most grizzled and cynical of tutors a thing or two, but @standupmaths1 has done exactly that. Most popular maths books, my own included, tread a pretty familiar path through the history of maths, throw out a

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Posted in gcse, quadratics, trigonometry.

It’s not often I have anything nice to say about EdExcel. I’ve usually found their exams to be the most predictable and least thought-provoking of all the boards (at least until they finally snapped in 2013 and let Kate the Photographer loose on an unsuspecting cohort). At GCSE, their advanced

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Posted in podcasts.

In this episode of Wrong, But Useful, @reflectivemaths and @icecolbeveridge…: Argue about the inferiority of statistics Give a number of the podcast: $e^{\frac{\pi}{2}} = i^i \approx 0.20788…$ Review @standupmaths’s excellent Things to Make and Do in the Fourth Dimension Investigate equable shapes in several dimensions, with reference to @tombutton’s MathsJam

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Posted in ask uncle colin, integration.

Dear Uncle Colin, I’ve been trying to work out $I = \int_0^{\frac \pi 4} x \frac{\sin(x)}{\cos^3(x)} \d x$ for hours. It’s the fifth time this week I’ve been up until the small hours working on integration and it’s affecting my work and home life. I’m worried I’m becoming a calcoholic.

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Posted in graphs, maths police.

A guest post from @FennekLyra, who is Eva in real life. Thanks, Eva! “Want to see something awful?” asked Agent Lyra1 suddenly, turning to her fellow maths agent and friend Dodo at the £16,000 question of Who Wants To Be A Millionaire? that both of them watched daily. “Oh come

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Posted in ask uncle colin, ninja maths.

Dear Uncle Colin Somebody told me that the sequences $\left \lfloor \frac {2n}{\ln(2)} \right \rfloor$ and $\left \lceil \frac{2}{2^{\frac 1n}-1} \right \rceil$ were equal up to the 777,451,915,729,368th term, and I shivered in ecstasy. Is there something wrong with me? — Sequences Considered Harmful When Agreeing Really Zealously Hi, SCHWARZ

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Posted in basic maths skills.

Every Friday afternoon, double maths with Mr Hutt: he would march up and down the classroom, barking: “Number seven: six times eight. Six times eight. Number eight: …” Twenty times tables questions, rapid-fire, scores kept. (One week, I fumbled $7\times 8$, blemishing my perfect score; Paul Edwards, on the other

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Posted in ask uncle colin, complex numbers, graphs.

Dear Uncle Colin, I was playing with parametric equations and stumbled on something Wolfram Alpha wouldn’t plot: $x=t^i;\, y = t^{-i}$. Does this curve really exist? Or am I imagining it? — A Real Graph? A Non-existant Drawing? Hi, ARGAND — what you’re trying to plot certainly exists; whether or

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Posted in gcse, there's more than one way to do it.

A student asks: I don’t get the Venn diagram method for highest common factor and least common multiple. Do you have any other suggestions? As it happens, I do. I’m assuming you’re OK with finding the prime factorisation of a number using (for example) a factor tree. In this example,

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