The Flying Colours Maths Blog: Latest posts

Ask Uncle Colin: The Area In Between

Dear Uncle Colin, I have the graphs of $y=\sin(x)$ and $y=\cos(x)$ for $0 < x < 2\pi$. They cross in two places, and I need to find the area enclosed. I’ve figured out that they cross at $\piby 4$ and $\frac{5}{4}\pi$, but after that I’m stuck! - Probably A Simple

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Dictionary of Mathematical Eponymy: Trémaux’s Algorithm

I recently had the chance to employ this one, but didn’t manage to: it turns out that four three-to-six-year-olds are not especially interested in putting down markers and following rules, they just want to run around the maize maze and say “maize maze” and make “amazing” jokes1 What is Tremaux’s

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Ask Uncle Colin: A Sum With An Unknown

Dear Uncle Colin, My textbook gives me an arithmetic sequence that starts $3 + 8 + 13 + \dots$, and asks me to find where the sum is 1575. I’ve got it down to $\frac{-1 \pm \sqrt{63,001}}{10}$, but I don’t know how to work out that square root without a

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The Mathematical Ninja and Logs Base 2

The student’s shoulder twitched slightly as he said “So I need to work out $\log_2(10)$…” and the crash of the cane against the table reminded him that the calculator was off-limits. “I think you can estimate that yourself,” said the Mathematical Ninja. “Uh… ok. There’s a change of base formula,

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Ask Uncle Colin: Factorising

Dear Uncle Colin, How would you go about factorising $6x^2 - xy - y^2 + 7x - y + 2$? - Argh! Getting Nowhere. Expression Simplification Impossible. Hi, AGNESI, and thanks for your message! I have, historically, not been a fan of these. However, I’ve recently come across a method

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Summing with Generating Functions

A nice challenge puzzle via Reddit: Find $\sum_{n=1}^{\infty} \frac{n2^n}{(n+2)!}$ There was a video attached to it that I didn’t watch, something about telescoping sums, but the moment I saw this, I thought: generating functions! Why would I think such a thing? The thing that jumped out at me was the

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Ask Uncle Colin: Why does the $ac$ method work?

Dear Uncle Colin, A while back, you shared an easy way to factorise nasty quadratics. Why does it work? Dutifully Indulging Students’ Curiousity & Reasoning In Maths. I’m Not A Nasty Teacher! Hi, DISCRIMINANT, and thanks for your message! Let’s start by recapping the method in the post, go through

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Captain Holt’s Seesaw

When Jake’s father (Bradley Whitford) comes to town, Jake is excited to see him, but Charles is wary of his intentions; Holt challenges Amy, Terry, Gina and Rosa with a brain teaser in exchange for Beyonce tickets. Brooklyn 99, S02 E18, Captain Peralta “Surely it isn’t that hard?” I have

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Ask Uncle Colin: Dividing Decimals

Dear Uncle Colin, I’m trying to work out $0.03 \div 0.1$. The answer is apparently 0.3, but I don’t understand why a division would make something bigger! Division Isn’t Very Intuitive, Decimals Especially Hi, DIVIDE, and thanks for your message! There are several ways to tackle this. I’ll start with

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Dictionary of Mathematical Eponymy: The Sieve of Sundaram

I am not a number theorist. I mean… well scratch that. I am not an especially knowledgeable number theorist1 but I do enjoy number theory when it’s around my level. The Sieve of Sundaram is about my level. What is the Sieve of Sundaram? OK, let’s start with the Sieve

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