# April, 2019

## 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

## Ask Uncle Colin: A round-robin

Dear Uncle Colin I’m organising a tournament with 16 teams, and wanted to arrange it in five stages, each consisting of four groups of four teams. However, I found that after three rounds, it wasn’t possible to find any groups without making teams play each other again! Why is that?

## Heads, Tails and Bumpsdaisy, revisited

At a recent East Dorset Mathsjam , the puzzle of two heads resurfaced: if you repeatedly flip a fair coin, how long (on average) do you have to wait until you get two heads in a row? Two fine answers are available here. However, the estimable Barney Maunder-Taylor went down

Dear Uncle Colin, I have to solve $5^x = 6 - 5^{1-x}$ - I understand it’s going to end up as a quadratic, but I can’t see how! - Explain, Uncle Colin, Like I Demand! Hi, EUCLID and thanks for your message! The key thing here is to spot that

## The Dictionary of Mathematical Eponymy: Daubechies Wavelets

Before I dive in to Daubechies wavelets, a confession: at university, Fourier series were the bane of my existence. I could do them, under duress, but in the same way as I set up the audio for Wrong, But Useful1: I had a recipe of steps I needed to follow,