January, 2017

How the Mathematical Ninja approximates $\sin(55º)$

“$0.819$,” said the Mathematical Ninja, in as weary a voice as the student used to say “I suppose you’re going to tell me how.” The nunchaku looked a little rusty, and the axe was in need of a good sharpening. The throwing knives could have done with a clear, and

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Ask Uncle Colin: A Stupid Expansion

Dear Uncle Colin, I've been challenged to expand $(x-a)(x-b)(x-c)…(x-z)$ so I can experience the 'joy of mathematics'. I've noticed that towards the end, one of the brackets is $(x-x)$ – does that mean the whole thing is zero? Is that the 'joy of mathematics they mean'? – Just Occupied Yesterday

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An innovative algebraic approach

Usually, when faced with a word problem, I take the most obvious approach and call it done. But then, sometimes, I read of an alternative approach that makes me go "Whoa." This is one of those times. Here's the problem: One day, a person went to a horse racing area.

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Ask Uncle Colin: How do I find the power?

Dear Uncle Colin, The equation $67.5 = 10(1.0915)^{10-n} + 30(1.0915)^{10-2n}$ cropped up in a question. Excel can solve that numerically, but I can't solve it on paper! Any ideas? Problems Occur When Exponentials Recur Hi, POWER, and thanks for your message! That's an ugly one. First thing: beware of the

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Wrong, But Useful: Episode 40

In this episode of Wrong, But Useful: @reflectivemaths and I are joined by special guest co-host Elizabeth A. Williams, who is @realityminus3 in real life (and Zeke, who is Zeke everywhere) Dave picks 367 as number of the episode, as it's the largest number whose square has digits in strictly

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An ex-straw-dinarily silly Fermi problem

Everybody sit down. Dominika has an important announcement. So…I have a confession to make. Despite the fact that I write maths comic strips, I’m actually a physicist. Pause for gasps of shock. Yes, terrible, I know. But physics in general has a little gem that I wish more people knew

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Ask Uncle Colin: How do I add things up?

Dear Uncle Colin, Is there an easy way to write series in sum notation? I have $1 + \frac{1}{2\sqrt{2}}+\frac{1}{3\sqrt{3}} + …$ but no real clue about how to put it into a compressed form. – Summing Is Giving Me Aneurysms Hi, SIGMA, and thanks for your message! I like to

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On a Crossnumber Clue

On a Crossnumber Clue In the Chalkdust Crossnumber #4, the deadline for which was last week, one of the first clues I looked at and thought “I can work that out easily enough” was this one: 27. The number of straight lines that go through at least two points of

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Ask Uncle Colin; A variable fraction

Dear Uncle Colin, I have a fraction, $\frac{x^2-x}{x-1}$, and I want to cancel it down to $x$ – but I'm not sure those are the same. Are they? – Got A Lot Of Interesting Sums Hi, GALOIS, and thanks for your message! The short answer is, yes and no. Everywhere

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A New Year’s Resolution For You (Only For Genius [sic])

Right, listen up, everyone. I know you've already made your new year's resolutions, and probably broken most of them by now, but I've got one for you to add to your list. It concerns images like this one: Anything with a picture of Einstein on it. Anything that says "only

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