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.
A student asks: I’m never sure whether I have to take the number that comes out of the normal distribution table away from 1. How do you know? It’s a familiar song: you’ve worked out your $z$-score (naturally, you remember that this means “how many standard deviations you are …
A student asks: Why are there so many equations for the variance? In S1, depending on the board you’re working with, you might need to know three equations for variance. For listed data, it’s: $\Var(X) = \frac{\sum x^2}{n} - \left(\frac{\sum x}{n}\right)^2$ For grouped data, it’s: …
A tweet from @GregSchwanbeck some time back asked: The setup is: one side of a square is tangent to a circle, and two corners of the square lie on the same circle. Which is larger: the perimeter of the square or the circumference of the circle? (My labels are different to Greg’s. That’s …
A reader asks: I need to solve $\frac ac \frac {NP}{N_0 + N} = mP$ for $N$, and I don’t know where to start. Help! I had a maths teacher in the early 90s who loved nothing more than making the class groan with bad jokes. If she showed up late, it was because she’d caught the rhom bus. …
I have a confession to make. One that will lower me seriously in the esteem of my 10-year-old nephew: I don’t really get Minecraft. Sorry, buddy. I’ve tried it. I love that you love it – honestly, creative games are awesome for your problem-solving skills and breaking down the …
Most of the time, my goal as a tutor is to help students stop hating maths and, if I’m lucky, to grudgingly accept that there are some good bits to it. I’m not here to indoctrinate anyone into becoming a mathematician unwillingly. And then sometimes, I get asked a question out of the …
“Where are they all coming from?” said the first, cocking the shotgun. “I don’t know,” said the second, “but I hope you’re a good shot.” “We haven’t covered this yet.” The first zombie lumbered into view, only instead of mindlessly …
Our second anniversary, and it’s a bit of a love-in. Sorry to disappoint. Colin and his partner have a new baby, Fred! Happy anniversary to us! Number of the podcast: $2+\sqrt{3}$, because it comes up in the Lucas-Lehmer test for Mersenne primes. A brief digression on the test, Mersenne primes …
I stumbled, recently, on a blog post about “Egoless programming”, a feature of a book called The Psychology of Computer Programming. The points struck me as good general advice – but also good advice for mathematicians at any level, so I thought I’d rework them here. …
How would I find the limit of $\frac{1}{x^2} - \cosec^2(x)$ as $x$ goes to 0? There are several valid approaches to this; two that spring to mind are L’Hôpital’s rule, which I like because it’s got an accent and two apostrophes, and series expansions, which I like because I like …
A reader (not, in fact, a Core 4 student) wrote in to ask: I have an ellipse in my spreadsheet program, using the formula $y = \frac ba \sqrt{a^2 - x^2}$, and I want to know the angle the normal to the ellipse makes with the horizontal at any value of $x$. Ah, the ellipse, my nemesis. We meet again. …
Someone on the internet asks: I don’t get why $\ln(e^x) = e^{\ln(x)}$. Can you explain? Of course I can! Or at least, I can try; the easy answer is to say ‘by definition’, but that doesn’t help you much. $\log_n(x)$ answers the question “what power would I raise $n$ to, …
There’s a lot of dead time to fill up when you’re covering the Boat Race. Once you’ve interviewed one gaggle of inebriated revellers from each of the two universities, you’ve interviewed them all. Once you’ve explained that the best strategy is to go faster than the …
A student asks: What’s the best way to use flashcards for revision? Flashcards are very popular in the USA, but have never really taken off over here. Any student with an exam to study for has a large stack of things they’re trying to learn: a question on one side, the answer on the …
At the East Dorset MathsJam Christmas party, @jussumchick (Jo Sibley in real life) posed the following question: There are two ways to draw a 16-gon with rotational symmetry of order 8 inside a unit circle, as shown. What’s the ratio of their areas? Typically, I look at this sort of question …
This is an excerpt from my upcoming book, The Maths Bible, (which will eventually be available from all good bookstores.) Udo of Aachen (c. 1200-1270) was a Benedictine monk, scholar, poet and mathematician. His best-known poetical work is Fortuna Imperatrix Mundi, which is usually know by its …
In honesty, I wasn’t expecting to enjoy this book. As a general rule, press releases that come my way – unless they’re very tightly targeted – can expect to find their way into my ‘spam’ folder. Matthew Watkins’ Secrets of Creation was a little lucky to …
“Things bounce six times higher on the moon!” James Corden, narrating Little Charley Bear I have some serious problems with the quality of the physics shown on CBeebies. I’m happy to accept anthropomorphised animals, the idea that all of the presenters live in the CBeebies house, …
One of the many people I look forward to seeing at big MathsJam is @pozorvlak, Miles in real life, whose name means ‘beware of the trams’ in Czech. When he’s not coding, pursuing the horrors of category theory, or juggling, he enjoys making his way up icy mountains. That’s …
A reader asks: I got an E in my mocks, but the universities I plan to apply for need at least a B - what do I do? PANIC! Next question. What’s that? Oh, OK. The Ninja says I have to write a proper answer. And if the Ninja says so… here are some steps you can take. 1. Stop panicking Your …
There was a post here, but it’s not here any more! Instead, it’s over at the Aperiodical, as part of their $\pi$ Day approximation challenge.
In this month’s action-packed podcast: Number of the podcast: 381,654,729, the only zero-less pandigital number such that the number formed by the first $n$ digits is divisible by $n$ This is Episode 24, so next month is our second anniversary. If you have any audio clips for us to include, …
The great @mathjem recently took advantage of snowy weather to post this question: On the one hand, it’s quite nice: using the weather and a popular culture reference to set a question on a semi-realistic topic. On the other, I have problems with it. Let’s brush aside ‘percentage …
@onthisdayinmath asks: Is it just me or has “factorise” (with s or z) suddenly become much more common term for “to factor” recently? Before I went to America, I had never seen factor used as a verb, at least in a mathematical context: you don’t ration a denominator, so …
A student asks: How do you integrate $\int_{0}^{\frac{\pi}{4}} \sec^4(x) \d x$? Yuk. Let me say that again for good measure: yuk. That’s going to need a trigonometric identity and, I think, a substitution. But that’s ok: we can do that. Let’s roll up our sleeves. Step 1: get rid of …
At a recent MathsJam, @brownmaths – who really should have known better – showed up with a calculator. Dear oh dear. His excuse was that it was in his teaching satchel, and he sometimes needed it to work out trigonometric functions (the Mathematical Ninja rolled his eyes, but I said fair …
I usually rankle when someone posts to MathsJam something that isn’t really MathsJam related - there’s been a spate of people in the USA who seem to think it’s aimed at primary school children, posting the sort of pathetic “If 2=4…” puzzles that plague Facebook. …
Don’t get me wrong: I love tutoring. As long as a student is putting in a genuine effort, I’m happy to forgive the odd “I don’t know” or “We haven’t been taught that.” And my students do put in the effort. I thank them for it. But there are some …
A student asks: Hi, I am currently doing Mechanics at college and I am finding it very confusing. What can I do to help get my head around the work? This is another slightly-hard-to-answer question; because I don’t know the student, or what s/he is struggling with, it’s really hard to …
In the first full-length podcast of 2015… Dave decides he’s not talking to me, which would make for another short one, if he meant it The number of the podcast: 3003, because of Singmaster’s conjecture @sherriburroughs (Sherri Burroughs in real life) asks: how can maths lovers …