# September, 2014

## Estimating $e$

Here at the Flying Colours Maths Blog, we’re never afraid to answer the questions on everyone’s lips – such as, why is $\left(1 + 9^{-4^{7\times 6}}\right)^{3^{2^{85}}}$ practically the same as $e$? When I say ‘practically the same’, I mean… well. 20-odd decimal places of $\pi$ are enough to get the

## The Maths Police Investigate: IndyRef edition

Gale surveyed the destruction with a face somewhere between disgust and admiration. Tunnock’s Caramel Wafer wrappers strewn across the room. A smell of haggis in the air. Bottles of whisky, half-drunk. Constable Beveridge… well, you wouldn’t say half-drunk. “You were up watching the referendum results last night, weren’t you?” Beveridge

## The Mathematical Ninja and the Supposedly Funny Cat

The Mathematical Ninja didn’t bother with a warning. The Mathematical Ninja didn’t even do that impressive whirry thing he does with a sword in each hand. No. The Mathematical Ninja conjured up a pistol and pulled the trigger – BANG! It was a blank, of course, but the student wasn’t

## Does attitude really equal 100%?

Every few weeks, this bit of motivational excrement does the rounds on twitter (I saw it here, but it comes around from all sorts of sources). For a start, what’s with the per cents? Per cents of what? You can’t just take a number that’s close to a hundred and

## How do I estimate?

A reader asks: There are some confusing questions in my maths textbooks. There is one question asking me to estimate the answers to the following maths problems but it doesn’t say whether we need to round the numbers to decimal places, or significant figures. So, I’d like to ask for

## Wrong, But Useful: Episode 18

An interview special, featuring our favourite Abel Prize nominee, @samuel_hansen! Sam is the brain behind Relatively Prime – which I consider some of the greatest maths radio journalism ever made1 and respectfully requests your donations towards it. It’s the only thing he’s ever done respectfully, so pay attention. You can

## L’Hôpital’s Rule – what it is and why it works

Let’s suppose, for the moment, you’re interested in the function $f(x) = \frac{\pi\sin(x)}{x}$. It’s a perfectly respectable function, defined everywhere except for $x = 0$, where the bottom is 0. The top is also zero there (because $\sin(0) = 0$), so its value is, strictly speaking, indeterminate – $\frac{0}{0}$ could,

## Long division considered harmful

Oh, for heaven’s sake. The Standards& Testing Agency has just released their new sample materials for Key Stage 2 (upper primary). Among other things in Mr Gove’s poisonous legacy is the insistence on everyone using formal methods of arithmetic, whether appropriate or not. The examples given in the test are:

## “Just invert and multiply”

Ours is not to reason why; just invert and multiply. – Anonymous Rule number one of Fractions club is: do NOT let the Mathematical Ninja hear you talking like that, otherwise you’re not going to have ears to hear rule number two. I mean – that is a way to