The Flying Colours Maths Blog: Latest posts

Ask Uncle Colin: Computing $\sqrt{2}$

Dear Uncle Colin, If I didn’t have a calculator and wanted to know the decimal expansion of $\sqrt{2}$, how would I be best to go about it? Roots As Decimals - Irrational Constant At Length Hi, RADICAL, and thanks for your message! There are several options for finding $\sqrt{2}$ as

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The Dictionary of Mathematical Eponymy: Banach’s Matchbox Problem

Stefan Banach was one of the early 20th century’s most important mathematicians - if you’re at all interested in popular maths, you’ll have heard of the Banach-Tarski paradox; if you’ve done any serious linera algebra, you’ll know about Banach spaces; if you’ve read Cracking Mathematics (available wherever good books are

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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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