The Flying Colours Maths Blog: Latest posts

Dictionary of Mathematical Eponymy: Mrs Perkins’ Quilt

“Lightly grease a 20x20cm baking tin with butter and spoon in the mixture. Press into the corners with the back of a spoon so the mixture is flat and score into 12 squares.” - BBC Good Food flapjack recipe by user nicolajlittle Hang on a minute - I thought, mid-baking.

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Ask Uncle Colin: Remainders

Dear Uncle Colin, I need to find four consecutive numbers such that the first is a multiple of 5, the second a multiple of 7, the third a multiple of 9 and the fourth a multiple of 11. Can you find such a number? - Summing Up Needs Zero Intelligence

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A “creative” integral

An interesting “creative” integral pointed my way by the marvellous @DavidKButlerUoA: Find $\int {\frac{1}{(1+x^2)^2}} \dx$ There are “proper” ways to do this - in his tweet, David shows a clever way to do it by parts, and suggests a trig substitution as an alternative. I want to show a third

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Ask Uncle Colin: An Arcsine Inversion

Dear Uncle Colin, I’m trying to invert $y = \arcsin\br{x^2 + 4x - 5}$, but I get stuck at $x^2 + 4x = \sin(y) + 5$. Any pointers? - All Routine Calculations Should Invert Naturally Hi, ARCSIN, and thanks for your message! Just before I dive into this, I have

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Fibonacci parity

On a recent1 episode of Wrong, But Useful, Dave noted that 33 of the first 100 Fibonacci numbers were even, 333 of the first 1000, and so on. My reaction wasn’t quite as it should have been: I said something like “well, yes, obviously”. While there’s a not-too-difficult reason behind

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Ask Uncle Colin: A Horrible-looking Limit

Dear Uncle Colin, I need to work out $\lim_{x\to\infty} \left\{ \left[ \frac{ 2^{1/x} + 8^{1/x} }{2} \right]^x \right\}$. The textbook says it’s four, but my engineering friends all get different answers. How would you work it out? - Giving Engineers Real Maths Analysis Is Naive Hi, GERMAIN, and thanks for

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Emergency Ask Uncle Colin: What happens now?

Dear Uncle Colin, I’m meant to be sitting my A-levels this summer and there’s an awful disease going around. I don’t know if school will be open next week or even if the exams will go ahead. I don’t know what that means for university. I’m scared. What do I

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The Mathematical Ninja and an Irrational Power

“The square root of two… I don’t even know how to say this. The square root of two to the square root of threeth power?” “$\sqrt{2}^{\sqrt{3}}$?” said the Mathematical Ninja. “I wouldn’t bother saying it, I’d just write it down.” “But what does it mean? I mean, I can just

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Wrong, But Useful: Episode 77

In this month's Pi Day Special episode, we're joined by @aap03102, who is Chris Smith in real life. We discuss: Negative primes Surdoku (look in issue $2^5$) Chris's dark past Chalkdust book of the year Book (or writing) ideas (I’m trying to compile a big list of maths things I

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Ask Uncle Colin: Long Division in Base 5

Dear Uncle Colin, I’ve been asked to show how to do $23241 \div 31$ in base 5 by long division - I can barely do it in base 10! Help! - Lots Of Number Games Hi, LONG, and thanks for your message! There are several steps to working a long

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