Posted in ask uncle colin, vectors.

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

Read More →
Posted in arithmetic.

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

Read More →
Posted in ask uncle colin, ranting.

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

Read More →
Posted in puzzles.

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

Read More →
Posted in ask uncle colin.

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 $c$

Read More →
Posted in podcasts.

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

Read More →
Posted in reviews.

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

Read More →
Posted in ask uncle colin.

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!

Read More →
Posted in ninja maths, probability.

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%?

Read More →
Posted in ask uncle colin.

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

Read More →