The Flying Colours Maths Blog: Latest posts

The heptagon puzzle

A few episodes of Wrong But Useful ago, Dave posed the problem: A regular unit heptagon1 has two different diagonal lengths, $a$ and $b$. Show that $a+b = ab$ Unusually, I didn't blog a solution. Sorry about that. A hat-rack trick I've come up with two approaches, but wanted to

Integration by parts: how you do it, and why it works

Integration by parts is one of the two important integration methods to learn in C4 (the other is substitution1 ). In this article, I want to run through when you do it, how you do it, and why it works, just in case you're interested. When you use integration by

There’s More Than One Way To Do It: Algebraic Division

Doing long division is like going to watch Raith Rovers play: you can force yourself do it, but why would you? I'm not going to show you the long division way. It's too much fuss to set out, and frankly I can't be bothered with it. There's a way I

Book review: Passion For Science

Fittingly, I'm sitting down to write this review while Google celebrates the 107th birthday of Grace Hopper - one of the first computer programmers, and - reputedly - the first person to debug a computer (by removing a moth from a vacuum tube). She wasn't the first computer programmer, though;

A student asks: I'm currently getting a G in maths and I need to get a C within 6 months - what am I going to do? Help! I wish I had a magic bullet for you, but I'm afraid the bad news is you'll need to work quite hard

Wrong, but Useful: Episode 9

In Episode 9 of Wrong, But Useful, @reflectivemaths (Dave Gale in real life) and I (sounding a bit like a Dalek) discuss: MathsJam conference @johndavidread's ideas on minches and mounds @srcav's post on multiplication, Colin's forthcoming post on division, and @robeastaway's thoughts on zequals The TES Maths Podcast - especially

PISA results: my thoughts

The 2012 PISA results came out yesterday, showing that the UK's place in the world rankings has remained almost unchanged over the last three years. It struck me, listening to the Today programme in a half-asleep stupor (as is my cliched, lefty-academic morning routine) that I didn't really know what

Call for guest posts

If you subscribe to the Sum Comfort newsletter, you might have picked up that I'm going to be a dad soon. I understand this will be pretty all-consuming for at least the next few months - which means I'm more than usually open to guest posts. Here are some guidelines

There’s More Than One Way To Do It: Equations of a circle

Depending on your AS-level maths exam board, you might encounter the equation of a circle in C1 (OCR) or C2 (everyone else). It's really just a restatement of Pythagoras' Theorem: saying $(x-a)^2 + (y-b)^2 = r^2$ is the same as saying "the square of the horizontal distance between $(a,b)$ and

How the gravitational slingshot works

The gravitational slingshot is something I'd heard about but had never bothered to look up - until now. It sounded like magic: you fire a spaceship towards a planet and (then a miracle occurs before) it comes out moving faster. It's how the Voyager spacecraft picked up enough speed to