# The Flying Colours Maths Blog: Latest posts

Dear Uncle Colin, I’m told that $f(x) = \frac{5x-7}{(x-1)(x-2)}, x\ne 1, x\ne 2$, and need to express it in partial fractions. My usual method would be to write it as $\frac{A}{x-1} + \frac{B}{x-2}$, multiply by $(x-1)(x-2)$ and substitute $x=1$ and $x=2$ to find $A$ and $B$ - but the definition

## Constructing the square root of 6

On Twitter, @RuedigerSimpson pointed me at an episode of My Favourite Theorem in which @FawnPNguyen mentioned a method for constructing $\sqrt{7}$: draw a circle of radius 4 construct a perpendicular to the radius at a distance of 3 from the centre the distance between the base of the perpendicular and

## Ask Uncle Colin: An Exponential Limit

Dear Uncle Colin, I need to work out the limit of $\frac{2^{3x} - 1}{3^{2x}-1}$ as $x \to 0$, and I don’t have any ideas at all. Do you? - Fractions Rotten, Exponents Generally Excellent Hi, FREGE, and thanks for your message! There are a couple of ways to approach this:

## A Harmonic Conundrum

This one came from user_1312 on reddit with a heading “This is a bit tricky… Enjoy!”. What else can we do but solve it? Let $m$ and $n$ be positive numbers such that $\frac{m}{n} = 1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{101}$. Prove that $m-n$ is a multiple

## Wrong, But Useful, Episode 73

In this month's episode of Wrong, But Useful, we talk to @AJMagicMessage, who is Andrew Jeffrey in real life, and one of the driving forces behind Maths Week England, which in 2019 is November 11th to 15th. Apologies for a few issues with feedback in this episode. Dave takes full

## Ask Uncle Colin: How many draws?

Dear Uncle Colin, I’m trying to figure out how many possible draws there are for the Champions’ League quarter-finals. There are eight teams involved, and let’s assume first leg home advantage doesn’t matter (so A vs B is the same as B vs A) and there’s no restriction on which

## Dictionary of Mathematical Eponymy: The Kovalevskaya Top

When I was about eight, my parents bought, as a Christmas gift for my brother and me, a “Jungle Gym”, plastic tubes and connectors that fit together to make whatever the imagination came up with, a sort of large-scale Meccano. My brother went out into the garden to build castles

## Ask Uncle Colin: Missing Planes

Dear Uncle Colin, I’m told that 70% of the aircraft that go missing in a certain country are subsequently rediscovered. Of those that are recovered, 60% have an emergency locator, and 90% of those that aren’t recovered, don’t have a locator. Supposing an aircraft has disappeared, what’s the probability it

## Summing Products

Some days your mind wanders into an interesting puzzle: not necessarily because it’s a difficult puzzle, but because it has familiar result. Then the puzzle becomes, how are the two things linked? For example, I had cause to add up all of the numbers in the times tables - let’s

## Wrong, But Useful: Episode 72

In this month's podcast, we're joined by @CoreMathsCat, who is Catherine van Sarloos in real life. We discuss: Number of the Podcast: 179 (balloons) Maths Week England is mid-November (11-16th). Catherine is involved in running a contest for it! Via Peter Rowlett: Women’s names Via Adam Atkinson: rounding up or