# December, 2019

## The Mathematical Ninja and the Cube Root of 13

A physicist. A calculator. The Mathematical Ninja’s face - what could be seen of it - was more snarl than feature. It’s quite tricky to hiss something that doesn’t have any sibilant consonants, but they hissed all the same: “The cube root of 13? You don’t need a calculator for

## Ask Uncle Colin: Where Should I Send Charitable Contributions?

Dear Uncle Colin, I know you don't ask for any money for your incessant blogging, and I've already bought Cracking Mathematics and The Maths Behind - how can I possibly repay you for your work? - Charities Helping Resist Inequality, Serving To Massively Ameliorate Society Hi, CHRISTMAS, and thanks for

## The Classwiz and the Normal Distribution

I realised today I’ve been advising my students… not wrong, exactly, but imprecisely. Capriciously. Unmathematically. Even through it was in statistics, where such things are usually tolerated, I felt it was worth putting it right. It was in a scenario such as this: The times an athlete takes to run

## Ask Uncle Colin: Some Messy Powers

Dear Uncle Colin, I’m told that $\frac{16^p \times 8^q}{4^{p+q}}=2^n$, and I need to find $n$ in terms of $p$ and $q$. How would I do that? $q$ Uppishly In $n$ Equation Hi, $q$UI$n$E1, and thanks for your message! There are several ways to approach this, as per always. Let’s start

## Barney’s triangles

A puzzle from @Barney_MT: Find angle BDC This turns out to be a bit more demanding than I expected. There are spoilers below the line, showing a solution that took rather more time and space than the final polished version does. Spoilers below the line! Adding in circles When I’ve

## Ask Uncle Colin: A Trig Inequality

Dear Uncle Colin, I have to find the values of $x$, between 0 and $\pi$ inclusive, where $2\cos(x) > \sec(x)$. My answer was $0 \le x \lt \piby 4$, but the answer also includes $\piby 2 \lt x \lt \frac{3}{4}\pi$. I don’t understand why! Stuck Evaluating Confusing And Nasty Trig

## A Trigonometric Puzzle

A puzzle that came to me via @realityminus3, who credits it to @manuelcj89: $\sin(A) + \sin(B) + \sin(C) = 0$ $\cos(A) + \cos(B) + \cos(C) = 0$ Find $\cos(A-B)$. There’s something pretty about that puzzle. Interestingly, my approach differed substantially from all of my Trusted And Respected Friends’. Spoilers below

## Wrong, But Useful, Episode 74

It’s time for the @BigMathsJam Wrong, But Useful! @stecks (Katie Steckles): Brouwer’s Fixed Point Theorem: “they said it’s a theorem, so I’ve got to believe it.” Mentions @jamesgrime. @christianp (Christian Lawson-Perfect): ordering cards to generate a fractal sequence. @peterrowlett (Peter Rowlett): transforming numbers problems into graphs. Mentions @alexcorner and @wtgowers.

## Ask Uncle Colin: A proof

Dear Uncle Colin, I have to prove that, if $a > b \ge 2$, then $ab > a + b$. I can see it must be true, but I can’t prove it! Any ideas? Questioning Everything Done Hi, QED, and thanks for your message! There are several ways to go

## Dictionary of Mathematical Eponymy: The Lutz-Nagell Theorem

One of the reasons I’m writing the Dictionary of Mathematical Eponymy is to introduce myself to new ideas, and to mathematicians I didn’t know about. To things I wish I knew more about. Elliptic curves are pretty high on that list. What is the Lutz-Nagell theorem? It’s sometimes - reasonably,