# The Flying Colours Maths Blog: Latest posts

## 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

Dear Uncle Colin, I struggled with a problem where you had 5 blue balls and x green balls, and the probability of picking two blue balls out of the bag was $\frac{5}{14}$. I can’t really see where to start! -Baffled About Likelihood, Lacking Startpoint Hi, BALLS, thanks for your message!

## On degrees

I gave a talk (some months ago now) on the history of $\pi$ (which is well discussed in my unreliable history of maths, Cracking Mathematics, available wherever good books are sold.) At one point, I put up a slide generally excoriating degrees as a measurement of angle, and stating that

## Ask Uncle Colin: A Set Square Mark

Dear Uncle Colin I just bought a new set square and noticed it had a couple of extra marks – one at seven degrees and one at 42 degrees. Have you any idea what those are for? – Don’t Recognise Extra Information Engraved on Calculus Kit Hi, DREIECK, and thank

## A tasty puzzle

Normally when I call something a tasty puzzle, it’s a lame local-paper pun about it being to do with cakes or something. In this case, it’s not even that. Sorry to disappoint. Instead, it’s a puzzle that came to me via reddit: Find $\sum_{i=1}^{10} \frac{2}{4^{\frac{i}{11}}+2}$. Eleventh roots? That’s likely to

## Ask Uncle Colin: Platonic Solids

Dear Uncle Colin, Why are there only five platonic solids? – Pentagons Look Awful. Try Octagons! Hi, PLATO, and thanks for your message! A platonic solid is a three-dimensional shape with the following rules: Each face is the same regular polygon The same number of edges meet at every vertex