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.
As I happened to be in London last week, I took an afternoon to visit the Science Museum and, especially, the Winton Gallery exhibit on Mathematics. Maths! In the Science Museum! What a treat! Or so I hoped. The Winton Gallery: Mathematics There’s a bit in Surely You’re Joking, Mr …
In this month’s Christmassy episode of Wrong, But Useful, @reflectivemaths and I discuss: Number of the podcast: 9 Shout outs to: @aap03102 (Chris Smith) for his maths newsletter @mathistopheles (Thomas Oléron Evans) and @fryrsquared (Hannah Fry) for sending me a copy of their book …
(Based on something that actually happened!)
Dear Uncle Colin, My teacher suggested that if you factorise a quadratic and add the brackets, you get the derivative. I am now too frightened to sleep. -- Quadratic Understanding Is Not Easy Hi, QUINE, and thanks for your message! To take a simple example, $x^2 + 5x + 6 = (x+2)(x+3)$ and, indeed, …
My dear friend @ajk44 pointed me at a puzzle on the excellent Nrich site1, and I enjoyed it enough to share my solution. (If you don’t want it spoiled, don’t read beyond the blockquote.) Four jewellers had respectively 8 rubies, 10 sapphires, 100 pearls and 5 diamonds. Each gave one gem …
Dear Uncle Colin, I’ve got a ratios question, and I don’t understand the solution. The question is: Three numbers, $x$, $y$, and $z$, have a sum of 871. The ratio $x:y$ is 4:5 and the ratio $y:z$ is 3:8. What is the value of $y$? Their solution is to say the ratio $x:y = 4:5 = …
The student sighed. “$\int x^3 e^{-2x} \dx$”, he said. “That’s going to be integration by parts. And it’s going to take three steps. What a pain.” “Aharr!” swashbuckled the Mathematical Pirate. “That’s what you think!” “It is …
Dear Uncle Colin, Sometimes, my professors write wrong things on the board, and I’m never sure whether to correct them. On one hand, I feel like I should respect them and their work; on the other, if I say nothing, I worry that my classmates are getting bad information. What should I do? - …
It’s your annual Wrong But Useful Big MathsJam Special! Recorded live, so the audio is a bit shaky in parts. @icecolbeveridge, @reflectivemaths and @peterrowlett discuss Tantrix with some excited background chatter Colin interviews @teakayb (Tom Briggs in real life), who’s at MathsJam with an Enigma …
Dear Uncle Colin, A question came up asking me to work out $4.5 + 1.5k = 18-3k$. Obviously, I can rearrange that to get $4.5k = 13.5$ - but how can I divide by 4.5 without a calculator? - Calculating A Number Turning On Ratio Hi CANTOR, and thank for the question! There are several ways to approach …
This is a guest post from Mark Ritchings, a maths tutor in Bury. A quadratic sequence is a sequence for which the $n$th term is $an^2+bn+c$. The constants $b$ and/or $c$ might be zero but $a$ definitely isn’t. The first term is $a\times 1^2 +b \times 1 + c = a+b+c$. The second term is $a …
Dear Uncle Colin, I noticed the sum of an arithmetic series and the formula for the area of a trapezium were very similar. How are they related? - Watching Every Interesting Equation, Recognised Something Trapeziumesque Regarding Arithmetic Sequence Sums Hi, WEIERSTRASS, Indeed, they are related, as …
In working out a recent blog post, I had cause to find the probability, in a standard normal distribution, of $z < -23$. Beyond “that’s a REALLY SMALL NUMBER”1, I was stumped. Could I get anywhere close mentally? A good question. Starting from the definition of the normal …
Dear Uncle Colin, Is there a reason you don’t use “Dr” in your author name? - Presumably Has Doctorate Hi, PHD! Thanks for your question. Yes, there are several reasons. The one I usually give is that my bank calls me Dr Beveridge and it makes me uneasy. It’s also slightly dubious …
Pick a number, any number1 Let’s say 24,876,028, one of my favourites in the 20-millions. I can tell by looking at it that it’s one more than a multiple of 9. It’s not that clever a trick: I just added up the digits (getting 37), and repeated the trick with that number (10), and …
Dear Uncle Colin, I’m struggling to make sense of questions about moments in M1. Can you help? -- Failing Equilibrium-Related Moments… All Torque! Hi, FERMAT! That’s a bit more general than the kind of question I usually answer, but no matter! Here’s the briefest theory of …
* Edited 2016-10-24 to add categories, just for Cav.
Dear Uncle Colin, I work in a call centre, which is run by the numbers. Every employee has to stay above a certain conversion rate, calculated as the number of successful deals resulting from their calls, divided by the number of times they have a call that doesn’t go to voicemail. My …
The Mathematical Ninja glanced at the Rubik Cube and paused. “And $45^3$ is…” A reach for the calculator. A flurry of colour. “Ow!” “91,125,” said the Mathematical Ninja, catching the cube on the rebound and swizzling it solved. “Only needed 12 that …
Dear Uncle Colin, I’ve been asked to find $2^{64}$ without a calculator, to four significant figures. How would you go about this? -- Large Exponent, Horrific Multiplication, Extremely Repetitive Hi, LEHMER! To get a rough answer, I’d usually start with the rule of thumb that $2^{10} …
In the October episode of Wrong, But Useful, @icecolbeveridge and @reflectivemaths have their habitual chat. Dave insults mechanics, then gets stroppy about Colin insulting stats The number of the podcast is 16, 40 and 64, because one number isn’t enough for Dave Dave visits a fete and gets …
Dear Uncle Colin, I’ve got a matrix, and I’m not afraid to use it. It’s $\begin{pmatrix} 3 & -5 \\ -4 & 2\end{pmatrix}$ Apparently, it has invariant lines. Those, I’m afraid of. How do I find them? -- Terrors About Rank, Safely Knowing Inverses Hi, TARSKI! An …
Via @DrTrapezio, an interesting question: Where do you even start with that mess? The answer to that, my friend, is you start in the middle and work your way out. You can think of this thing as a series of transformations: Start with $y = |x|$ Move it down one unit1 and take the modulus of the …
Dear Uncle Colin, I’ve got three points: $A$, with a position vector of $(2\bi + 4\bj)$, $B$, with a position vector of $(6\bi + 8\bj)$ and $C$, with a position vector of $(k\bi + 25\bj)$, and they all lie on the same straight line. I have to find $k$, and I don’t know where to start! -- …
A lovely curiosity came my way via @mikeandallie and @divbyzero: Isn’t that neat? If I use an estimate $p = 3.142$, then this method gives $\pi \approx p + \sin(p) = 3.141\ 592\ 653\ 6$, which is off by about $10^{-12}$ – even better than Shanks suggests. So, why does it work? It’s …
Dear Uncle Colin, My research has determined that female adults have a mean overhead reach of 208.5cm, with a standard deviation of 8.6cm, and follows a normal distribution. I wanted to know the probability that the mean overhead reach of 50 female adults would lie between 180cm and 200cm and got a …
Don’t get me wrong, The Dorset Echo is one of my favourite local newspapers. They have been kind enough to feed my ego on several occasions, and even if their headlines sometimes don’t quite reflect the gist of the story, I appreciate that. This time, though, they’ve gone too far.1 …
Dear Uncle Colin, I have a system of equations I can’t solve! $x + y + z = 100$; $.08x +.1y +.2z = 12$; $y - z = 25$ I keep tripping up on the decimals and negative signs! -- We’re Extremely Stressed Solving Equations Linear Hello, WESSEL! My best advice for not tripping over the …
I have a tendency to write about interesting questions from a ‘here’s how you do it’ point of view, which must give the impression that I never get confused1. To try to dispel that, I wanted to share something that came up in an Oxford entrance paper (the MAT from 2010, if you’re interested). It’s …
Dear Uncle Colin, I’m looking for the equation of a curve that goes through the points $\left(10, \frac{1}{64}\right)$ and $\left(100, \frac{1}{32} \right)$, as – as $x$ gets large – approaches 1. How do I go about it? Always Silence Your Mobile Phone Typing Out Tricky Equations …