The Flying Colours Maths blog has been running posts twice weekly since 2012, covering maths from the basics to… well, the most advanced stuff I have a clue about.
Here they all are, sorted by date. Some day, other ways to filter them will be possible.
Compared to regular small print, it’s pretty big, but compared to the four-panel, faux-war-era comic story (disaster strikes, protagonist calls Rent-A-Loan*, cash magically appears and they all live happily ever after), you could easily overlook it. You might even look at the bottom of the …
Learning the rough value of a few key numbers worth knowing can make ninja maths a lot more impressive later on - especially if you know how roughly how rough the rough values are. A little bit about the tables below: I’m giving you decimals to two sig figs, the best simple fraction I know, …
The end of the week already? Doesn’t it fly? Well, what can I help you with this week? Just drop me a comment below and I’ll do what I can to answer it.
I am too good for philosophy and not good enough for physics. Mathematics is in between. - George Polya, author of How To Solve It, one of my favourite maths books.
-or- matching coefficients for fun and profit I bluffed my way through completing the square at A-level. I guessed, dropped minus signs, and dropped marks all the way. It was only once I started teaching it that I figured out completing the square. Let me share it with you. Completing the square …
Difficulty: ** Impressiveness: **** If you do A-level maths, you do an awful lot of integration. You integrate polynomials, trig functions, partial fractions, exponentials, parametric curves, products of these… and get nice analytical answers. Here, let me provoke controversy: Unless …
It’s the Easter break, time to make good on all those promises to put the work in before the exams! How can I help you this week? What’s bothering you? Where are you stuck? Let me know in the comments and I’ll get back to you as soon as I can!
There’s a dark cloud looming. It’s already April and the AS and A2 maths exams are unusually early this year. So, the question is, what can you do to revise effectively without driving yourself crazy? Here are my top three tips for getting on top of the material rather than bogged down …
Difficulty: (simple version) *** (advanced version) ***** Impressiveness: ***** Accuracy: *** If you’re a statistician, you quite often end up working out powers of numbers just a little less than 1. What’s the probability of rolling a pair of dice ten times and never getting a double …
It’s that time of the week again! What’s been on your mind? What’s giving you a headache? As always, drop your questions in the comments box and I’ll get back to you as swiftly as I can!
We all agree that your theory is crazy, but is it crazy enough? - Niels Bohr
A conjecture both deep and profound Needs a proof that the circle is round. In a paper by Erdős Written in Kurdish A counter-example is found. One of my favourite questions to ask students is “what’s a circle?” because I get to play “so that means this is a circle!” …
Some of the secrets of the mathematical ninja are pretty pointless, when you come down to it: after all, we have machines for most of these things. The divisibility tricks are useful (as far as I can see) only in a very specific circumstance: when you’re deciding whether to cancel down a …
It’s that time of the week again! What’s been on your mind? What’s giving you a headache? As always, drop your questions in the comments box and I’ll get back to you as swiftly as I can!
Right! That’s it. I’m mad as hell and I’m not going to take it any more. If one more student looks at a question and says “I don’t know where to start!” I’m going to… I’m going to… I’m going to FROWN and look at them VERY CROSSLY. …
Difficulty: ** Impressiveness: **** (Many thanks to Swar for pointing me at this one - and challenging me to explain it well!) It’s surprisingly easy to square numbers near 50. Here’s the recipe: 1. Find the difference between your number and 50. (If you’re looking at 46, …
It’s that time of the week again! What’s been on your mind? What’s giving you a headache? As always, drop your questions in the comments box and I’ll get back to you as swiftly as I can!
Happy Pi Day! mu-tant cow pi by janemariejett In the American date format, today is 3.14 - a pretty good approximation to $\pi$, which (as any fule kno) is the ratio between a circle’s diameter and circumference. It’s also the focus of most of the jokes about maths, because - get this - …
The trick: someone says ‘what’s 7.5 squared?’ and - mentally squaring in a flash - you say: 56.25. Squaring halves Squaring halves is really easy if you know your times tables. Here’s the method: Take your number and find the whole numbers immediately above and below. If …
It’s that time of the week again! What’s been on your mind? What’s giving you a headache? As always, drop your questions in the comments box and I’ll get back to you as swiftly as I can!
I was sent this by my friend and colleague TeaKay from Blogstronomy, and I’ve adapted the puzzle slightly to make the sums a little bit nicer. A curve has the equation $y = (x-2)^2 - n^2$. The area bounded by the co-ordinate axes and the curve in the first quadrant is equal to the area bounded …
A couple of weeks ago, a news story flashed by me on twitter: 49% of the UK have slower-than-average broadband. It was followed more or less immediately by a swathe of snipey comments saying ‘isn’t that the definition of an average?’ To which the smart-arse answer is, no, there is …
It’s that time of the week again! March already! What’s been on your mind? What’s giving you a headache? As always, drop your questions in the comments box and I’ll get back to you as swiftly as I can!
“He’s not Judge Judy and executioner!” - Danny Butterman, Hot Fuzz There’s a reason statistical experiments are sometimes called trials: they take up a lot of time and are pretty much the epitome of suffering. What’s that? Oh, sorry. No, apparently, it’s because …
Until about three years ago, I had literally no idea how to factorise nasty quadratics. I would turn straight to the quadratic formula, go bing bang boom and say ’there, job done.’ This was a very effective short-cut - I got a long way with my ignorance - but I’m faintly …