April, 2015

Wrong, But Useful: Episode 25

Our second anniversary, and it's a bit of a love-in. Sorry to disappoint. Colin and his partner have a new baby, Fred! Happy anniversary to us! Number of the podcast: $2+\sqrt{3}$, because it comes up in the Lucas-Lehmer test for Mersenne primes. A brief digression on the test, Mersenne primes

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The Egoless Mathematician

I stumbled, recently, on a blog post about "Egoless programming", a feature of a book called The Psychology of Computer Programming. The points struck me as good general advice -- but also good advice for mathematicians at any level, so I thought I'd rework them here. I've made minor adjustments

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Finding a limit

How would I find the limit of $\frac{1}{x^2} - \cosec^2(x)$ as $x$ goes to 0? There are several valid approaches to this; two that spring to mind are L'Hôpital's rule, which I like because it's got an accent and two apostrophes, and series expansions, which I like because I like

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Normals to an ellipse: a Core 4 masterclass

A reader (not, in fact, a Core 4 student) wrote in to ask: I have an ellipse in my spreadsheet program, using the formula $y = \frac ba \sqrt{a^2 - x^2}$, and I want to know the angle the normal to the ellipse makes with the horizontal at any value

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Why logs and exponentials undo each other

Someone on the internet asks: I don't get why $\ln(e^x) = e^{\ln(x)}$. Can you explain? Of course I can! Or at least, I can try; the easy answer is to say 'by definition', but that doesn't help you much. $\log_n(x)$ answers the question "what power would I raise $n$ to,

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Picking a station

There's a lot of dead time to fill up when you're covering the Boat Race. Once you've interviewed one gaggle of inebriated revellers from each of the two universities, you've interviewed them all. Once you've explained that the best strategy is to go faster than the other boat, there's not

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Using flashcards effectively

A student asks: What's the best way to use flashcards for revision? Flashcards are very popular in the USA, but have never really taken off over here. Any student with an exam to study for has a large stack of things they're trying to learn: a question on one side,

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A MathsJam Masterclass

At the East Dorset MathsJam Christmas party, @jussumchick (Jo Sibley in real life) posed the following question: There are two ways to draw a 16-gon with rotational symmetry of order 8 inside a unit circle, as shown. What's the ratio of their areas? Typically, I look at this sort of

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Udo of Aachen: Lives of the Mathematical Ninja

This is an excerpt from my upcoming book, The Maths Bible, (which will eventually be available from all good bookstores.) Udo of Aachen (c. 1200-1270) was a Benedictine monk, scholar, poet and mathematician. His best-known poetical work is Fortuna Imperatrix Mundi, which is usually know by its choral title, O

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I teach in my home in Abbotsbury Road, Weymouth.

It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby.

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