# February, 2014

## Wrong, But Useful: Episode 12

The dozenth episode of @reflectivemaths (Dave Gale in real life) and @icecolbeveridge (Colin Beveridge) chatting (and/or ranting) about the maths we’ve seen this month. Which includes: A brief discussion of dozenal Colin gives blood and gets woozy; Dave tried it once The big question: why is maths important? In which

## Multiplying halves by halves: Secrets of the Mathematical Ninja

The student, by now, knew better than to pick up the calculator. “There’s got to be a way of doing that quickly.” The Mathematical Ninja looked a little disappointed; he’d built an elaborate electromagnetic pulse generator for the express purpose of killing calculators in a mysterious flash. “You’re right,” he

## Why is the sum of five consecutive squares never a square?

In a recent Wrong But Useful podcast, @reflectivemaths (who is Dave Gale in real life) asked the audience to: Prove that the sum of five consecutive square numbers is never a square. This one’s a bit easier than it looks: I chose to call the middle number of the five

## Linear Interpolation: There’s More Than One Way To Do It

If I had £35 every time a student said “I don’t get linear interpolation,” I’d have pretty much the same business model as I do right now. Everyone knows it’s something to do with finding medians and quartiles, and something to do with the class width and… stuff. Some can

## Why negative and fractional powers work the way they do

Most of the students I help have a pretty good grasp of the three straightforward power laws: $(x^a)^b = x^{ab}$ $x^a \times x^b = x^{a+b}$ $x^a \div x^b = x^{a-b}$ So far, so dandy – and usually good enough if you’re hoping for a B at GCSE. The trouble comes

## Figuring out roots of horrible numbers

“$1296$?!” said the student. “They want me to find the fourth root of $1296$?” “Evidently,” I said. The air turned, for a moment, blue. “Well, how about factorising it?” A different shade of blue. A whirring of pencil. A mutter of 648, a grumble of 324, a harrumph of 162,

## A student asks: what’s it like to do a maths degree?

A student asks: I’m currently studying further maths A-level – and I love it! I want to obtain a degree in it. Could you provide an insight into what it’s like? I’m happy to share my experiences, although they’re probably specific to St Andrews, for me, in the late 90s

## Blazing through the Binomial Expansion

“Where’s the Mathematical Ninja?” asked the student. “He’s… unavoidably detained,” I said. In fact, he was playing Candy Crush Saga. But sh. “What can I help you with today?” “Well, you know the binomial expansion…?” “Intimately,” I said. “Well, I got it pretty well at C2… but now we’re doing