The Flying Colours Maths Blog: Latest posts

A puzzle from Sheena

A puzzle that came to me via @sheena2907: Choose two numbers, $x$ and $y$, uniformly from $[0,1]^2$. What’s the probability that $\frac{x}{y}$ rounds to an even number? What’s the probability that it rounds down to an even number? As always, spoilers below the line. Rounding One of my best approaches

Read More

Ask Uncle Colin: Flipping Signs

Dear Uncle Colin, Is there a rigorous explanation of why the direction of the inequality changes when you flip the sign? - Fuzzy Logic, Inequality Puzzle Hi, FLIP, and thanks for your message! Here are my best efforts at a rigorous explanation; I’d be interested to read anyone else’s go

Read More

Bending a long bar

A nice thinker from Futility Closet: A rail one mile long is lying on the ground. If you push its ends closer together by a single foot, so that the distance between them is 5279 feet rather than 5280, how high an arc will the rail make? Feel free to

Read More

Wrong, But Useful: Episode 79

In this, the penultimate episode of Wrong, But Useful, we’re joined by @karenshancock (who is Karen Hancock in real life). We discuss: A scoring system for an online quiz round. The Big Mathoff What is a surd? Currently reading Ratio by Michael Ruhlman - a cookery book that starts from

Read More

Ask Uncle Colin: A Fractional Equation

Dear Uncle Colin, I’m trying to solve $\frac{x}{x-1} = \frac{1}{x-1}$. I think the answer should be 1, but my teacher disagrees. What do you think? - First Results Are Contradicting Teachers’ - Is One Nonsense? Hi, FRACTION, and thanks for your message! It’s tempting, here, to multiply both sides by

Read More

Binet’s formula and Haskell

This is an extended version of my entry in the Lockdown Mathoff at the Aperiodical Binet’s formula1 is a lovely way to generate the $n$th Fibonacci number, $F_n$. If $\phi = \frac{1}{2}\left(\sqrt{5} + 1\right)$, then $$F_n = \frac{ \phi^n - (-\phi)^{-n} }{\sqrt{5}}$$ Haskell and computation The main reason I’m writing

Read More

Ask Uncle Colin: The Empty Product

Dear Uncle Colin, Why does $0! = 1$ and not 0? - Nothing Is Logical Hi, NIL, and thanks for your message! My best explanation for this - by which I mean, the one I can get some people to accept, goes like this: $4! = 4 \times 3 \times

Read More

Dictionary of Mathematical Eponymy: The Quine-McCluskey Algorithm

There was a Fields Medallist named Dan Quillen, after whom are named several things in topics I’ve never head of. Other than Quillen, so far as I can tell, the only mathematical eponyms beginning with Q relate to Willard Van Ormine Quine. I know him from Godel, Escher, Bach, where

Read More

Ask Uncle Colin: Rotating vectors

Dear Uncle Colin, I need to find a unit vector in the xy-plane that makes an angle of 45 degrees with the vector $3\bi + 4\bj$. How would you do that? - Don’t Enjoy Maths Of Integer Vectors Rotating Enough Hi, DEMOIVRE, and thanks for your message! I can think

Read More

Some puzzles from Cav

A couple of puzzles that came my way via @srcav today: Cav’s solutions to this one are here; mine are below the line further down. Interesting angle puzzle https://t.co/UN13XwwY3o pic.twitter.com/NyaQL0H7wE — Cav (@srcav) July 8, 2019 And to this one, here Have a go yourself before you read on! I’ve

Read More

Sign up for the Sum Comfort newsletter and get a free e-book of mathematical quotations.

No spam ever, obviously.

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.

On twitter