# December, 2015

## Ask Uncle Colin: A Modulo Mistake

Dear Uncle Colin, I wanted to work out $3^{41}\mod 13$: Wolfram|Alpha says it's 9, but MATLAB says it's 8. They can't both be right! What gives? MATLAB Obviously Doesn't Understand Logical Operations Hi, MODULO! First up, when computers disagree, the best thing to do is check by hand. Luckily, you

## A trigonometric coincidence

"Hm," I thought, "that's odd." I don't often work in degrees, but the student's syllabus insisted. And $\sin(50º)$ came up. It's 0.7660, to four decimal places. But... I know that $\sin\left(\frac 13 \pi\right)$, er, sorry, $\sin(60º)$ is 0.8660 -- a difference that's pretty close to $\frac 1{10}$. Which got me

## Wrong, But Useful: Episode 31

In this month's festive WBU, Colin and Dave discuss... Bill's second birthday and train set Colin's latest book is due out any day. First number of the podcast: 998 (days since our first recording) Colin gloats about Spoof My Proof and Dave chews on sour grapes Second number of the

Dear Uncle Colin, I'm having trouble getting my head around sum notation! I can't tell whether $\sum_{n=0}^{6}{5}$ means $0\times5 + 1\times 5 + ... + 6\times 5$ or $0 + 1 + 2 + ... + 6$ or $5 + 5 + 5 ... + 5$. Wolfram|Alpha just gives me

## Is applied maths less satisfying than pure?

A question, some time ago, from my favourite Egyptologist on Twitter: Is applied maths less satisfying than pure? @ColinTheMathmo @icecolbeveridge #mathcult — Liz Hind (@drbhind) April 14, 2014 There's a very simple answer to this question: it doesn't just depend on who you're asking, it may also depend on what

## Ask Uncle Colin: A hellish trigonometric identity

Dear Uncle Colin, @CmonMattTHINK unearthed the challenge to prove that: $\tan\left( \frac 3{11}\pi \right) + 4 \sin\left( \frac 2{11}\pi \right) = \sqrt {11}$. Wolfram Alpha says it's true, but I can barely get started on the proof and I'm worried no-one will like me. Grr, Really Obnoxious Trigonometry Has Evidently

I've always had a soft spot for the Countdown numbers game, a challenge pitched just perfectly right for my mental capacities. It would take a very good numbers game to displace Countdown in my heart. Mathador is a very good numbers game1 with similarities to Countdown: you're given a batch

## “Destiny”

The following puzzle/trick came up on Futility Closet, one of my favourite sites for recreations. Here's how they describe it: Arrange cards with values ace through 9 in a row, in counting order, with the ace on the left. Take up a card from one end of the row —

Dear Uncle Colin, Do you have any advice about Cambridge interviews? I have one coming up. How About Wanting Kings (If Not, Girton) Hello, HAWKING! My Cambridge interviews were a couple of decades ago, so I don't know how current my advice is. A few things: be ready to demonstrate

## Review: The Joy of $x$, by Steven Strogatz

In terms of tone and style, The Joy of $x$ is an absolute delight -- Strogatz has a knack for finding the right analogy and the right anecdote that is the envy of maths writers everywhere. It's an enjoyable read, and I'd recommend it to anyone who thinks "I'd love