July, 2014

$\left(1+ \frac {1}{n}\right)^n$

This doesn't appear to work on all models of calculator. Let me know whether yours handles it properly... "I saw this thing about Euler's identity," said the student, and the words "ut" and "oh" forced themselves, unbidden, into my head. You've maybe seen it: it's $e^{\pi i} + 1 \equiv

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A student asks: How do you simplify surds?

A student asks: How could I simplify a sum like $(\sqrt 3+\sqrt 2)(\sqrt 3-\sqrt 2)$? Great question! The trick is to treat it like it's an algebraic bracket, like this: $(x + y)(x - y) = x^2 + yx - xy - y^2$ But then you've got $+yx -xy$ in

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A trigonometric trick: Secrets of the Mathematical Ninja

"Have you seen this trick?" asked the student. "If you know all three sides of a right-angled triangle, you can estimate the other angles - $A \simeq \frac{86a}{\frac b2 + c}$!" The Mathematical Ninja thought for a moment, and casually threw a set-square into the wall, millimetres from the student's

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Euclid the Game: level 20

Note: since I wrote this post, level 20 has moved to level 23. It may move again in the future, I suppose. Rather than keep updating, it's the one with the tangent to two circles. I LOVE Euclid, the game - it's a brilliant, interactive way to get students (and

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A proof of the sine rule

Here's a nice use of circle theorems: ever wondered why the sine rule works?

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A Ninja Masterclass

"Boom!" said the Mathematical Ninja, as the smoke cleared and the student jumped. Shell-shocked, he looked again at the whiteboard. "Wh-what just happened?" The Mathematical Ninja sighed. "OK, one more time. We're trying to estimate the size of the shapes you'd need to cover a sphere with $n$ patches, which

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Tamil Fractions

A friend asks for REASONS: THAERTTHUGAL n. The smallest named fraction in the ancient Tamil language = 1/2323824530227200000000. — The QI Elves (@qikipedia) April 7, 2014 A who to the what now? A twelve-letter word, a thaerrhugaL, representing a number somewhere in the region of twenty-three ninety-ninths of a sextillionth.

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Ten books that stayed with me

I don't quite remember who asked this, but at some point someone asked me to list ten books that have stayed with me. 1066 And All That - Sellar and Yeatman I've a beat-up copy of this I borrowed (what do you mean stole?) from my parents, and it's one

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Wrong, But Useful: Episode 16

In this month's episode of Wrong, But Useful, @reflectivemaths (Dave Gale) and I discuss: How Dave thinks Baby Bill should learn to count Decimal time McDonalds apple pies - Made 15:26. Ready 15:36 Discard 16:56 "School lunch could save you up to £437 a year. Only 1% of packed lunches

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