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.
It’s a best-seller in France, apparently: the wild-haired but immaculately-dressed Fields Medallist’s story of how he and his colleague solved the Landau damping problem. But therein lies my difficulty with it: I don’t know about, or especially care about, the Landau damping …
In a departure from the norm, Wrong But Useful tries its first panel game. In a completely original format, our intrepid podcasters trade lies in a panel game entitled Spoof My Proof. On Colin’s team: @christianp (Christian Lawson-Perfect) and @dragon_dodo (Dominika Vasilkova) On Dave’s …
Dear Uncle Colin, In one of Randall Munroe’s What If? articles he says that the maths of finding a random point on a sphere is a bit hairy. Can’t you just pick a random latitude and longitude? -- Surely Places Have Equal Random Expectations You would think so, wouldn’t you, SPHERE? …
“‘The book that could change football for ever’ – The Times,” screams the garish orange front cover. Noted football experts Malcolm Gladwell and Billy Beane shower it with praise. Apparently everything I know about football is wrong. Despite all of the dubious hype, The …
“Arr!” said the Mathematical Pirate. “Pieces of eight!” said the Mathematical Pirate’s parrot. “How many pieces of eight?” “Seven!” “That’ll be… seventy and ten minus twenty and four, making fifty and six!” …
Dear Uncle Colin, I’m finding it hard to understand why, when you multiply two negative numbers together, you get a positive number. I accept that it’s true, but I was brought up to believe that two wrongs don’t make a right. -- Positive Equals A Negative Otherwise? There is a …
“Prediction is very difficult, especially if it’s about the future” – Niels Bohr (attrib.) Like everybody else, I had no idea who Nate Silver was until I started following his 538 column in the run-up to the 2008 US Presidential election. Like everyone else, I took some …
“$\ln$”, said the student, “of 123,456,789.” He sighed, contemplated reaching for a calculator, and thought better of it. “18.4,” said the Mathematical Ninja, absent-mindedly. “A bit more. 18.63.” The student diligently wrote the number down, the …
Dear Uncle Colin, A friend of mine told me that $1 + 2 + 4 + 8 + … = -1$. Is he crazy, or is there something going on here? -- Somehow Enumerating Ridiculous Infinitely Extended Sum Dear SERIES, There are a couple of ‘proofs’ of this non-fact that fall down basically because your …
Even as someone who owes at least some of his maths skills to computer games (I played L in the late 80s and would love to see it resurrected, and there’s a lot to be said for the mental arithmetic in something like Football Manager), my heart still sinks a little when I see something …
You know the ridiculous kind of pseudo-context question that makes you go ‘Why doesn’t Lisa get a proper hobby rather than timing her friends doing jigsaw puzzles?’? You could replace pretty much all of them with “A mathematician is trying to be clever by…”. In …
Dear Uncle Colin, I noticed that $2^{\frac{1}{1,000,000}} = 1.000 000 693 147 2$ or so, pretty much exactly $\left(1 + \frac{1}{1,000,000} \ln(2)\right)$. Is that a coincidence? Nice Interesting Numbers; Jarring Acronym Dear NINJA, The easiest way to see that it’s not a coincidence is to check …
It’s genuinely difficult to write an innovative maths book, something that’ll teach even the most grizzled and cynical of tutors a thing or two, but @standupmaths1 has done exactly that. Most popular maths books, my own included, tread a pretty familiar path through the history of maths, …
It’s not often I have anything nice to say about EdExcel. I’ve usually found their exams to be the most predictable and least thought-provoking of all the boards (at least until they finally snapped in 2013 and let Kate the Photographer loose on an unsuspecting cohort). At GCSE, their …
In this episode of Wrong, But Useful, @reflectivemaths and @icecolbeveridge…: Argue about the inferiority of statistics Give a number of the podcast: $e^{\frac{\pi}{2}} = i^i \approx 0.20788…$ Review @standupmaths’s excellent Things to Make and Do in the Fourth Dimension …
Dear Uncle Colin, I’ve been trying to work out $I = \int_0^{\frac \pi 4} x \frac{\sin(x)}{\cos^3(x)} \d x$ for hours. It’s the fifth time this week I’ve been up until the small hours working on integration and it’s affecting my work and home life. I’m worried I’m …
A guest post from @FennekLyra, who is Eva in real life. Thanks, Eva! “Want to see something awful?” asked Agent Lyra1 suddenly, turning to her fellow maths agent and friend Dodo at the £16,000 question of Who Wants To Be A Millionaire? that both of them watched daily. “Oh come on, now; that question …
Dear Uncle Colin Somebody told me that the sequences $\left \lfloor \frac {2n}{\ln(2)} \right \rfloor$ and $\left \lceil \frac{2}{2^{\frac 1n}-1} \right \rceil$ were equal up to the 777,451,915,729,368th term, and I shivered in ecstasy. Is there something wrong with me? -- Sequences Considered …
Every Friday afternoon, double maths with Mr Hutt: he would march up and down the classroom, barking: “Number seven: six times eight. Six times eight. Number eight: …” Twenty times tables questions, rapid-fire, scores kept. (One week, I fumbled $7\times 8$, blemishing my perfect …
Dear Uncle Colin, I was playing with parametric equations and stumbled on something Wolfram Alpha wouldn’t plot: $x=t^i;\, y = t^{-i}$. Does this curve really exist? Or am I imagining it? -- A Real Graph? A Non-existant Drawing? Hi, ARGAND – what you’re trying to plot certainly …
A student asks: I don’t get the Venn diagram method for highest common factor and least common multiple. Do you have any other suggestions? As it happens, I do. I’m assuming you’re OK with finding the prime factorisation of a number using (for example) a factor tree. In this …
Dear Uncle Colin, I’ve been challenged to find the area of the intersection of three circles while drawing a Venn diagram. I don’t know where to start! -- Triangle Unpredictably Rounded; I’m No Genius For a moment, TURING, I thought there wasn’t a problem in this problem, but …
“So that works out to be $10^{1.6}$,” said the student, reaching for the calculator – and, of course, recoiling as the Mathematical Ninja yelled “yeeha!” and lasso-ed it out of her hand. “Forty,” he said. “Too high by half a percent or so. 39.8.” …
Dear Uncle Colin, I have an equation to solve: $\ln(x^2) = 2 \ln(4)\, x \ne 0$. I tried to solve it by applying the log laws: $2 \ln(x) = 2 \ln(4)$, so $x=4$. However, a bit of thought shows that $x=-4$ is also a solution – but that doesn’t seem to come out of the laws! My eyes have gone …
Until fairly recently, I had always done the kind of differential equations you see in Core 4 the same way: separate, integrate, substitute, celebrate. I have taught any number of students the dance; many of them have boogie-woogied their way into a correct answer in exams. But there’s a …
Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions – and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can. Dear Uncle Colin, I have a problem I just …
A few months ago, @preshtalwalkar at Mind Your Decisions showed off how he’d advise someone to work out $43 \times 67$ using one of my favourite tricks, the difference of two squares. In fact, that’s how I’d have approached the question at first, too: the two numbers are 12 either …
Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions – and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can. Dear Uncle Colin, I’m having trouble …
The estimable Barney Maunder-Taylor asked at MathsJam: How come the inverse square law leads to elliptical orbits and equal area swept in equal time? I only know the answer to one of those questions. The differential equations for the inverse square laws work out to be: $\diffn{2}{r}{t} - r \left …
Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions – and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can. Dear Uncle Colin, I’ve been given a …