# The Flying Colours Maths Blog: Latest posts

## Ask Uncle Colin: A dangling rope

A Hanging Rope Dear Uncle Colin, I’m designing a small cathedral and have an 80-metre long rope I want to hang between two vertical poles. The poles are both 50 metres high, and I want the lowest point on the rope to be 20 metres above the ground. How far

## Wrong, But Useful: Episode 63

In this month’s installment of Wrong, But Useful, Dave and I are joined by @honeypisquared, who is Lucy Rycroft-Smith in real life. We discuss: Mathematical board games, including The Mind Camel Cup Qwinto Number of the podcast: Lucy doesn’t like numbers so we don’t have one. Does your collection of

## What I learnt from a STEP Speedrun

I’ve been doing some work on STEP recently – maths exams used mainly for entrance at Cambridge and Warwick, who want some way to differentiate between very good A-level candidates. When I was in Year 13, I had an interview – in fact, two interviews – at Cambridge; at one

## Ask Uncle Colin: Integrating $\sec$ and $\cosec$

Dear Uncle Colin, I keep forgetting how to integrate $\sec(x)$ and $\cosec(x)$. Do you have any tips? – Literally Nothing Memorable Or Distinctive Hi, LNMOD, and thanks for your message! Integrating $\sec(x)$ and $\cosec(x)$ relies on a trick, and one the average mathematician probably wouldn’t come up with without a

## The Dictionary of Mathematical Eponymy: Ackermann’s function

For 2019, I’m trying an experiment: every couple of weeks, writing a post about a mathematical object that a) I don’t know much about and b) is named after somebody. These posts are a trial run – let me know how you find them! The chief use of the Ackermann

## Ask Uncle Colin: A Strange Simultaneous Equation

Dear Uncle Colin, I have the simultaneous equations $3x^2 – 3y = 0$ and $3y^2 – 3x = 0$. I’ve worked out that $x^2 = y$ and $y^2 = x$, but then I’m stuck! – My Expertise Relatedto1 Simultaneous Equations? Not Nearly Enough! Hi, MERSENNE, and thanks for your message!

## Sticks and Stones

Because I’m insufferably vain, I have a search running in my Twitter client for the words "The Maths Behind", in case someone mentions my book (which is, of course, available wherever good books are sold). On the minus side, it rarely is; on the plus side, the search occasionally throws

## Ask Uncle Colin: A Factorial Sum

Dear Uncle Colin, I have been given the series $\frac{1}{2} + \frac{1}{3} + \frac{1}{8} + \frac{1}{30} + \frac{1}{144} + …$, which appears to have a general term of $\frac{1}{k! + (k+1)!}$ – but I can’t see how to sum that! Any ideas? – Series Underpin Maths! Hi, SUM, and thanks

## A Christmas Decagon

Since it’s Christmas (more or less), let’s treat ourselves to a colourful @solvemymaths puzzle: Have a go, if you’d like to! Below the line will be spoilers. Consistency The first and most obvious thing to ask is, is Ed’s claim reasonable? At a glance, yes, it makes sense: there’s a

## Ask Uncle Colin: Some Ugly Trigonometry

Dear Uncle Colin, How do I verify the identity $\frac{\cos(\theta)}{1 – \sin(\theta)} \equiv \tan(\theta) + \sec(\theta)$ for $\cos(\theta) \ne 0$? – Struggles Expressing Cosines As Nice Tangents Hi, SECANT, and thanks for your message! The key questions for just about any trigonometry proof are "what’s ugly?" and "how can I