# The Flying Colours Maths Blog: Latest posts

## Ask Uncle Colin: A Complex Conundrum

Dear Uncle Colin, I'm told that $z=i$ is a solution to the complex quadratic $z^2 + wz + (1+i)=0$, and need to find $w$. I've tried the quadratic formula and completing the square, but neither of those seem to work! How do I solve it? – Don't Even Start Contemplating

## Mr Penberthy’s Problem

It turns out I was wrong: there is something worse than spurious pseudocontext. It's pseudocontext so creepy it made me throw up a little bit: This is from 1779: a time when puzzles were written in poetry, solutions were assumed to be integers and answers could be a bit creepy…

## Ask Uncle Colin: My partial fractions decompose funny

Dear Uncle Colin, I recently had to decompose $\frac{3+4p}{9p^2 – 16}$ into partial fractions, and ended up with $\frac{\frac{25}{8}}{p-\frac{4}{3}} + \frac{\frac{7}{8}}{p-\frac{4}{3}}$. Apparently, that's wrong, but I don't see why! — Drat! Everything Came Out Messy. Perhaps Other Solution Essential. Hi, there, DECOMPOSE, and thanks for your message – and your

## Wrong, But Useful: Episode 44

In this month's episode of Wrong, But Useful, @reflectivemaths1 and I are joined by consultant and lapsed mathematician @freezingsheep2. We discuss: Mel's career trajectory into 'maths-enabled type things that are not actually maths', although she gets to wave her hands a lot. What you can do with a maths degree,

## Review: The Mathematics Lover’s Companion, by Edward Scheinerman

There is a danger, when your book comes plastered in praise from people like Art Benjamin and Ron Graham, that reviewers will hold it to a higher standard than a book that doesn't. That would be unfair, and I'll try to avoid that. What it does well This is a

## Ask Uncle Colin: an arctangent mystery

Dear Uncle Colin, In an answer sheet, they've made a leap from $\arctan\left(\frac{\cos(x)+\sin(x)}{\cos(x)-\sin(x)}\right)$ to $x + \frac{\pi}{4}$ and I don't understand where it's come from. Can you help? — Awful Ratio Converted To A Number Hello, ARCTAN, and thank you for your message! There's a principle I want to introduce

Last week, I wrote about the volume and outer surface area of a spherical cap using different methods, both of which gave the volume as $V = \frac{\pi}{3}R^3 (1-\cos(\alpha))^2(2-\cos(\alpha))$ and the surface area as $A_o = 2\pi R^2 (1-\cos(\alpha))$. All very nice; however, one of my most beloved heuristics fails

## Ask Uncle Colin: how big do the patches on a football need to be?

Dear Uncle Colin, I’m trying to sew a traditional football in the form of a truncated icosahedron. If I want a radius of 15cm, how big do the polygons need to be? — Plugging In Euler Characteristic’s Excessive Hello, PIECE, and thank you for your message! Getting an exact answer