# May, 2018

## Ask Uncle Colin: Sketching in 3D

Dear Uncle Colin Do you have any tips for sketching three-dimensional vectors? Every time we have an A-level question, my teacher says "draw a diagram!" but I don't know how to draw in 3D. - Got A Useless Sketching Situation Hi, GAUSS, and thank you for your message! Three-dimensional vectors

## Back in 1940…

That @solvemymaths is an excellent source of puzzles and whathaveyou: Meanwhile, back in 1940 when everything was basically shit... pic.twitter.com/A5eKXOunFC — Ed Southall (@solvemymaths) October 7, 2017 How would you find $\sqrt[3]{\frac{1-x^2}{x}}$ when $x=0.962$, using log tables or otherwise? I would start by trying to make the numbers nicer: I

Dear Uncle Colin, I'm sitting my GCSE Maths starting tomorrow. What will the grade boundaries be? - First Exams Are Redoubtable Hi, FEAR, I'm writing this, believe it or not, in early February1. I'm not even sure this summer's GCSE papers have been written yet, but I am going to

## A Handshake Problem From the MathsJam Shout

One of the puzzles in the MathsJam Shout looked impossible, so obviously I sat down with Mr Miller and had a go at it. I don't have it in front of me, but it went something like: A couple hosts a party to which five other couples are invited. At

## Ask Uncle Colin: A Complex Roots Problem

Dear Uncle Colin, I had a question in an exam that gave a cubic, $f(x) = x^3 - 8x^2 + cx + d$, with roots $\alpha$, $\beta$ and $\gamma$. When plotted on an Argand diagram, the triangle formed by the three roots has area 8. Given that $\alpha=2$, find $c$

## Wrong, But Useful: Episode 56

In Episode 56 of Wrong, But Useful, we're joined by @zoelgriffiths (Zoe Griffiths), maths communicator from Think Maths. Zoe had her poem e, to thee, x in @chalkdustmagazine recently, and did a set about misleading statistics at @aeoud (An Evening Of Unnecessary Detail) Bad polls and fake stats, including this

## Review: Genius at Play, by Siobhan Roberts

It turns out, I made an error in Cracking Mathematics. Not (in this case) a mathematical or historical error, although there are plenty of those1 but an error of etiquette: my potted biography of John Horton Conway emphasised the Game of Life above the rest of his work; I imagine

## Ask Uncle Colin: A binomial puzzler

Dear Uncle Colin, I'm practicing for the Oxford PAT and have been asked how many terms of the binomial expansion would be needed to determine $(3.12)^5$ to one decimal place? I don't really know where to start. - Knows Expansions (Binomial); Lacks Explanations Hi, KEBLE, and thanks for your message!

## The Mathematical Ninja and the SSNs

A professor - according to Reddit - asked their class how many people you'd need to have in a room to be absolutely certain two of them would have Social Security numbers1 ending in the same four digits (in the same order). 10001, obviously. How about a probability of 99.9%?

## Ask Uncle Colin: Auxiliary Equations With Repeated Roots

In this post, I swap liberally between d-notation and '-notation for derivatives. Deal with it. Dear Uncle Colin, Why do we have to treat second-order ODEs differently when the auxiliary equation has a repeated root? Something Or Other Defies Expectations Hi, SOODE, and thanks for your message! First, some background