# The Flying Colours Maths Blog: Latest posts

## A triangle puzzle

Like everyone else on Twitter, I’m a sucker for a nice-looking question, and @cshearer41 is a reliable source of such things. I particularly liked this one: There are two equilateral triangles inside this semicircle. What’s the area of the larger one? pic.twitter.com/Nvy01z2j5f — Catriona Shearer (@Cshearer41) November 7, 2018 Straight

## Ask Uncle Colin: an irrational power

Dear Uncle Colin, How would you work out something like $(-1)^\pi$? Doesn’t Everyone Miss Out Irrational Values Reckoning Exponents? Hi, DEMOIVRE, and thanks for your message! In the words of the politician: difficult, difficult, lemon difficult. One the one hand there is one answer that seems sensible - but on

## Dictionary of Mathematical Eponymy: Elo ratings

As I write this, classical chess’s top two players are Magnus Carlsen of Norway (rated 2835) and the USA’s Fabiano Caruana, who has a rating of 2832. Very close! But what do the rankings mean? FIDE1 uses the Elo rating system, a methodical - and mathematical - system for distilling

Dear Uncle Colin, In a culture where people have children until they have a daughter and then stop, what proportion will be daughters? * Families Retain Extra Girls Evidently Hi, FREGE, and thanks for your message1 ! Spoiler alert: it’s a half. There are several ways to see this, and

## On Estimating

An exam question was recently brought to my attention: students were asked to estimate $31.28^2$. Whoosh “$31^2 = 961$ and $31.5^2 = 992.25$, so it’s about 978.” “Very good, sensei, but no marks. Uhuhuh, put that down - you need to take it up with the exam board, not with

## Ask Uncle Colin: The Polar Express(ion)

Dear Uncle Colin, I have the polar equation $\theta = k$, and I want to turn it into rectangular coordinates. I worked it out to be the line $y = x \tan(k)$, but the solution says it’s only a half-line. Why is that? Perplexed Over Line And Radius Hi, POLAR,

## Wrong, But Useful: Episode 66

In this month’s episode of Wrong, But Useful, we’re joined by @cshearer41, who is Catriona Shearer in real life. We discuss: LaTeX (time to fight again) Mathematical sign language More interesting ‘bad graphs’ than the obvious howlers you usually see on the internet. Via @peterrowlett: Some people think statistics has

## The Mathematical Ninja and $\arctan(0.4)$

It took the Mathematical Ninja a little longer than normal; the student had managed to rummage around in her bag and lay a finger on the calculator before simultaneously feeling her arm pulled away by a lasso and hearing "0.3805. Or, as a one-off, since the question is asking for

## Ask Uncle Colin: A Six-Digit Square

Dear Uncle Colin, I’m told a six-digit number, ABC,DEF1, is a perfect square such that DEF is 8 times ABC. How do I find this number? - Very Interesting, Except That Eight Hello, VIETE, and thanks for your message! This is as much of a typographical challenge as it is

## Tactical Voting

As a progressively more adamant Europhile, I was pleased to learn that the UK would take part in next month’s European Parliament elections1. As an amateur psephologist, I was delighted. Rather glibly, I responded to someone asking whether one needed to vote tactictally in these elections by saying “no, it’s