The Flying Colours Maths Blog: Latest posts

Resolving an Unfinished League

Last week, the English Football League season was cancelled, with standings decided on a points-per-game basis in League One and League Two1 In League One, that led to Wycombe Wanderers leaping into the playoffs at the expense of Peterborough, who had accrued the same number of points but played a

There is no Ask Uncle Colin today #strike4blacklives

In support of #strike4blacklives, there is no Ask Uncle Colin today. Please see Shut Down STEM to learn more. I will be spending the time I would have spend working reading Superior by Angela Saini in an attempt to fill some of the gaps in my knowledge. Black lives matter.

Cav, Catriona and some hexagons

It’s always fun to tackle a puzzle from one of Cav’s posts - in this case, a Catriona Shearer puzzle; it looks like my solutions are completely unrelated to his, although in reality I tend to sneak the odd peek and take some inspiration1 I also liked that Cav shared

Ask Uncle Colin: Two Numbers Close To 1

Dear Uncle Colin, How do I tell which is larger, $2^{-10^{-20}}$ or $1 - 2^{-10^{20}}$? - Unexpectedly Narrow Interval… Thank You! Hi, UNITY, and thanks for your message! As you’ve doubtless realised, both of those are “pretty much 1”. The question is, which is closer? As usual, there are several

The Dictionary of Mathematical Eponymy: Randolph diagrams

A second-in-a-row Dictionary of Mathematical Eponymy post about Boolean logic today – and another example of a Very Neat Diagram. What is a Randolph diagram? You’ve seen - at least, I hope you’ve seen - Venn diagrams. Beastly things. I would chuck them out the window if I could, they

Ask Uncle Colin: A difference of polynomials

Dear Uncle Colin, Can two polynomials be equal everywhere in some non-trivial interval $[a,b]$ but not equal elsewhere? - Lacking A Good Reasonable Answer, No Good Explanation Hi, LAGRANGE, and thanks for your message! The answer is “no”, but to explain why, I need to give you a few pieces

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

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

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

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