# The Flying Colours Maths Blog: Latest posts

## Ask Uncle Colin: A Mess of Logs

Dear Uncle Colin, I have to show that $$-\frac{x}{2} = \ln (\sqrt{1+e^x} - \sqrt{e^x }) + \ln (\sqrt{1+e^{-x}} + 1)$$. I can't get it anywhere near the right form! - Proof Of It Not Coming - Any Reasonable Explanation? Hi, POINCARE, and thanks for your message! That's a bit of

## Exchange rates on board

"Three teas, please," said the passenger ahead of me in the queue. The Armorique was due in Plymouth any minute, and tea was of the essence. "That's £4.65, or €5.601." Hang on a moment, I thought, remembering to order my own tea as well. 560 isn't a multiple of 3.

## Maths, Magnus Carlsen, and Making Decisions

An emergency blog post about chess, of which I know nothing. This is not meant as serious analysis; think of it more as “here are some topical maths ideas you can throw at your classes.” So, I looked up the Elo ratings for the chess world championship players: in rapid

## Ask Uncle Colin: A Cubic That Won’t Come Good

Dear Uncle Colin, I'm told that $$x\sqrt{x} - 5\sqrt{x} = 2$$ and I have to find $$x - 2\sqrt{x}$$. Everything I try seems to make it worse! Any ideas? Mastering A Cubic - Help Is Needed Hi, MACHIN, and thanks for your message! At first glance, that's a strange one.

## All The Maths Podcasts

Since @reflectivemaths wasn't at Big MathsJam and @samuelhansen was, the MathsJam Special is a bit different this year.

## The Mathematical Ninja and the Variable Volume

The student, at the third time of asking, navigated the perilous straits of negative powers and fractions of $\pi$ and came to rest, exhausted, on the answer: "$r^3 = \frac{500}{\pi}$," he said. The Mathematical Ninja stopped poking him with the foam sword (going soft? perhaps. Or perhaps this student needed

Dear Uncle Colin, As I progress through my maths education, I notice that the people around me are getting smarter and smarter. How do I keep my head up when everyone is brighter than me? I'm Mightily Put Off Seeing Their Outstanding Results Hi, IMPOSTOR, and thanks for your message!

It's always Alice and Bob. Why must it always be Alice and Bob? In any case, the two of them are tossing coins Until they hit a particular sequence: Alice until she hits a head then a tail, Bob until he hits two heads in a row. Counter-intuitively, Alice will

## Ask Uncle Colin: Why is it called “completing the square”?

Dear Uncle Colin, Why is it called "completing the square"? To me, it looks like you're taking something away from a square. - Some Quadratics, Understandably, Are Requiring Explanation Hi, SQUARE, and thanks for your message! Completing the square involves taking a quadratic such as $x^2 + 6x + 5$

## ILATE vs LIATE

Some time ago, I recommended the mnemonic "LIATE" for integration by parts. Since you have a choice of which thing to integrate and which to differentiate, it makes little sense to pick something that's hard to integrate as the thing to integrate. With that in mind, you would look down