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 know that $x^3 e^{-x}$ approaches zero as $x$ approaches infinity - I can see it from the graph - but I don’t really understand why? Can you help? Of course I can! However, it’s going to take us into the murky depths of analysis, and we’ll need to understand the …
What does a blogger do when he has a stinking headache, no ideas, and a commitment to write a blog post? Of course! A lazy list post! Luckily, it’s a lazy list post that gives a shout-out to people whose stuff I enjoy, so it’s not all bad. News, roundups and so on Well, you’ve got to start with The …
A reader asks: Is it easier to predict every game in the first round of a tournament1, or to pick the eventual winner? There’s a competition run by Sky, which is free to enter; you win £250,000 if you correctly predict the scores in six Premier League games. It’s free to enter. A quarter …
Someone on the internet asks: What percentage of the natural numbers have the digit ‘seven’ in them? This is going to sound like a weird answer: it’s 100%. I know, I know: you can point at 42 and 100 and 986,543,210 and 666,666,666,666,666 and at least a handful of others - so …
In this month’s WBU spectacular: Big MathsJam is coming up - book quickly! The Relatively Prime Series 2 Kickstarter closes today. Donate quickly! Dave’s got a chapter in a book - order quickly! Colin sails into the wind (virtually) Dave’s moving house over half term: what maths …
The Mathematical Pirate took one look at the piece of paper attached to the dock. “They’re BANNING formula triangles?! By order of @srcav?!” He swished his sword around. “Let me figure out where he lives, I’ll show him.” “He lives… inshore, cap’n” said the $n$th mate. “It’s too dangerous.” “Can we …
There’s a constant refrain in the Flying Maths Classroom, these days, of “I can’t quite remember…” Whether it’s a trig identity or $21 \div 7$, the outbreak of amnesia in the quiet suburbs of Weymouth seems close to epidemic proportions. What can one tutor do, …
A reader asks: I keep dropping marks in tests by making silly mistakes. Is that something I just have to get used to? Great question! I have, in a box of ancient relics upstairs, one of my GCSE mock papers. On the front of it is the number “100”, scribbled out and replaced by …
Solve $\sqrt{|x|-3} > x-4$ Difficult, as the man said. Difficult, difficult, lemon difficult. It’s not that it’s tricky to solve it - it’s just… fiddly. Let’s start by drawing the graphs. The right-hand side is easy enough: it’s a straight line with gradient 1, through the point $(0,-4)$. The …
“We do these things… not because they are easy, but because they are hard.” - John F. Kennedy I love a challenge. I go out of my way to do Hard Sums in my head, in the hope of one day matching the Mathematical Ninja’s prowess. I run long distances. I juggle childcare with a tutoring business. I work …
Here at the Flying Colours Maths Blog, we’re never afraid to answer the questions on everyone’s lips - such as, why is $\left(1 + 9^{-4^{7\times 6}}\right)^{3^{2^{85}}}$ practically the same as $e$? When I say ‘practically the same’, I mean… well. 20-odd decimal places of $\pi$ are …
Gale surveyed the destruction with a face somewhere between disgust and admiration. Tunnock’s Caramel Wafer wrappers strewn across the room. A smell of haggis in the air. Bottles of whisky, half-drunk. Constable Beveridge… well, you wouldn’t say half-drunk. “You were up watching the referendum …
The Mathematical Ninja didn’t bother with a warning. The Mathematical Ninja didn’t even do that impressive whirry thing he does with a sword in each hand. No. The Mathematical Ninja conjured up a pistol and pulled the trigger - BANG! It was a blank, of course, but the student …
img.wp-image-4136 { padding: 15px; } [caption id=“attachment_4136” align=“alignright” width=“227”] Yes, it’s coincidence[/caption] Every few weeks, this bit of motivational excrement does the rounds on twitter (I saw it here, but it comes around from all …
A reader asks: There are some confusing questions in my maths textbooks. There is one question asking me to estimate the answers to the following maths problems but it doesn’t say whether we need to round the numbers to decimal places, or significant figures. So, I’d like to ask for …
An interview special, featuring our favourite Abel Prize nominee, @samuel_hansen! Sam is the brain behind Relatively Prime - which I consider some of the greatest maths radio journalism ever made1 and respectfully requests your donations towards it. It’s the only thing he’s ever done …
Let’s suppose, for the moment, you’re interested in the function $f(x) = \frac{\pi\sin(x)}{x}$. It’s a perfectly respectable function, defined everywhere except for $x = 0$, where the bottom is 0. The top is also zero there (because $\sin(0) = 0$), so its value is, strictly speaking, indeterminate - …
Ours is not to reason why; just invert and multiply. - Anonymous Rule number one of Fractions club is: do NOT let the Mathematical Ninja hear you talking like that, otherwise you’re not going to have ears to hear rule number two. I mean - that is a way to divide fractions, and done correctly it …
“Yarr,” said the Mathematical Pirate. “Ye’ll have plundered a decent calculator, of course?” “Er… well, I bought it from Argos, but… aye, cap’n! A Casio fx-83 GT PLUS!” “A fine calculator,” said the Mathematical Pirate. “One that offers you at least three ways to factorise cubics.” “Really!? I …
In a class recently, I came across a circle theorem problem I’m certain I’ve seen before, but that I didn’t know off the top of my head how to solve. Here it is; have a go at it if you’d like to.  The examiners’ expectation was clearly that the student would know that PD:PA = PB:PC - and neither …
“$\cos^{-1}(0.93333)$, said the student. A GCSE student, struggling a little; the Mathematical Ninja bit his tongue rather than correct him to $\arccos$ or to $\frac {14}{15}$; he also accepted, grudgingly, the answer was going to be in degrees. “Maybe 21 bad degrees?” “21.04”, said the student. …
“[James McEvoy] is an unashamed geek - he was reading a book on physics, as you do, to see if it could improve his performance.” - Radio 5 swimming commentator “You need some kind of accountancy degree to work out what each of them needs to do in the final round…” - BBC 2 Gymnastics commentator. If …
Didn’t July seem to go on for ever? What’s that? Oh. Um, yeah, delayed Episode 17 because @reflectivemaths (Dave Gale) decided a family holiday was more important than your listening pleasure. What a selfish man. This month, we talk about: Dave’s failure to send a postcard The …
The Mathematical Ninja woke up at 8:58, and opened his other eye. “$e^{12}$?” asked his alarm clock. “$160,000$,” said the Mathematical Ninja, and sat bolt upright. He leapt out of his sleeping corner, somersaulted across the room, landing in front of the whiteboard just as the student arrived. …
This is something that struck me the other day when someone asked me about the difference between university maths and sixth-form maths: every time a student moves between educational levels, “what maths is” undergoes a dramatic change. This is based on my memories of school and is likely to be …
A student asked: What’s the link between the Poisson formula and the binomial? … and I started to cry a little bit. Infinitely many trials You use the Poisson distribution when you have events happening at a constant rate, on a continuous time-frame - as opposed to the binomial, which …
This doesn’t appear to work on all models of calculator. Let me know whether yours handles it properly… “I saw this thing about Euler’s identity,” said the student, and the words “ut” and “oh” forced themselves, unbidden, into my head. …
A student asks: How could I simplify a sum like $(\sqrt 3+\sqrt 2)(\sqrt 3-\sqrt 2)$? Great question! The trick is to treat it like it’s an algebraic bracket, like this: $(x + y)(x - y) = x^2 + yx - xy - y^2$ But then you’ve got $+yx -xy$ in the middle there, which adds up to nothing: …
“Have you seen this trick?” asked the student. “If you know all three sides of a right-angled triangle, you can estimate the other angles - $A \simeq \frac{86a}{\frac b2 + c}$!” The Mathematical Ninja thought for a moment, and casually threw a set-square into the wall, …
Note: since I wrote this post, level 20 has moved to level 23. It may move again in the future, I suppose. Rather than keep updating, it’s the one with the tangent to two circles. I LOVE Euclid, the game - it’s a brilliant, interactive way to get students (and their teachers) thinking …