# July, 2016

## Wrong, But Useful: Episode 36

In this month’s episode, @reflectivemaths and @icecolbeveridge discuss: Dave is baffled by the idea of the Anniversary Games but happy to have a reduced workload We agree on the name and age of the podcast Number of the podcast: 36, the smallest non-trivial square triangle number. Colin has a new

## Ask Uncle Colin: How do I multiply mixed fractions?

Dear Uncle Colin, I’m OK at multiplying simple fractions by numbers and fractions by each other, but I don’t understand how to multiply mixed fractions together. Help! — Variations In Numerators Can Upset Learners Understanding Maths Hello VINCULUM1 ! I think I’m on record as saying that mixed fraction are

## The Mathematical Ninja and the Nineteenths

“Look,” said the student, “we all know how this goes down. A nasty-looking fraction comes out of the sum, I reach for the calculator, you commit some act of exaggerated violence and tell me how you, o wondrous one, can do it in your head.” “You’re not as dumb as

## Ask Uncle Colin: A STEP vectors problem

Dear Uncle Colin, I’m struggling with this STEP question. The first two parts are fine — equality holds when there is some constant $k$ for which $a = kx$, $b = ky$ and $c=kz$, and part (i) follows directly from the original inequality. I can get an answer to part

## Why $\phi^n$ is nearly an integer

This article is one of those ‘half-finished thoughts’ put together late at night. Details are missing, and — in a spirit of collaboration — I’d be glad if you wanted to fill them in for me. The estimable @onthisdayinmath (Pat in real life) recently posted about nearly-integers, and remarked that

## Ask Uncle Colin: What is $\tan(1º)$?

Dear Uncle Colin, In my trigonometry homework, I’ve been asked to find the exact value of $\tan(1º)$. I have no idea where to start. Help! — A Nice, Gentle Little Exercise Hello, ANGLE. That’s an evil question, on many levels. It’s doable, but it’s not at all easy. In this

## The Maths Police Investigate: For The Love Of God, Make It Stop

The cadets are at it again. Thanks to @dragon_dodo and @FennekLyra. Agent Lyra and Agent Dodo were bored. After several weeks of suspending Gale’s desk in bizarre positions, fencing on the office chairs and sneakily pilfering Beveridge’s ginger beer, they had quite run out of things to do. Draped over

## Ask Uncle Colin: Can you prove $\sin(2x) \equiv 2\sin(x)\cos(x)$?

Dear Uncle Colin, I find it easier to remember trigonometric identities if I can ‘see’ how they fit together. I’m expected to know that $\sin(2x) \equiv 2\sin(x)\cos(x)$, but haven’t been able to prove it. Any ideas? — Geometry? Right Angles? How About Medians? Hi, GRAHAM! My favourite proof jumps out

## Brutal simultaneous equations

I recently became aware of the IYGB papers, available from Madas Maths. Like the Solomon papers, they’re intended to stretch you a bit — they’re ranked by difficulty from standard to extremely hard. My student, being my student, demanded we go through one of the extremely hard ones. There were