# January, 2019

## Ask Uncle Colin: An Implicit problem

Dear Uncle Colin, I have to find the points $A$ and $B$ on the curve $x^2 + y^2 - xy =84$ where the gradient of the tangent is $\frac{1}{3}$. I find four possible points, but the mark scheme only lists two. Where have I gone wrong? I've Miscounted Points Like

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## A Matrix Definition of a Line

Every so often, I see a tweet so marvellous I can't believe it's true. Then I bookmark it and forget about it for months, until I don't know what to write next. An example is @robjlow's message from June: Aren't determinants wonderful? pic.twitter.com/vxIKeS4Lrq — Robert Low (@RobJLow) June 26, 2018

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## Ask Uncle Colin: Powers and Remainders

Dear Uncle Colin, I'm told that $2^a \equiv 9 \pmod{11}$. How do I find $a$? - Powers And Stuff, Calculating And Learning Hi, PASCAL, and thanks for your message! As so often, there are (at least) two reasonable ways to tackle this: a brute force way and an elegant way.

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## Factfulness

Sometimes, someone dies and you think “it’s a pity their time came.” And sometimes, someone dies and you think “oh no! We needed them.” Hans Rosling (for me) was in the second camp: someone using maths for social good, someone combining graphic design, storytelling and numbers to make the world

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## 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

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## 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

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## 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

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## 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

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## 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

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## 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!

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##### Where do you teach?

I teach in my home in Abbotsbury Road, Weymouth.

It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby.