The Flying Colours Maths Blog: Latest posts

Ask Uncle Colin: A Curve

Dear Uncle Colin, I’m given that a curve has equation $y = ax^3 + bx^2 + cx + 1$. It has a turning point at $\left( -1, \frac{11}{3} \right)$ and an inflexion point when $x=2$. How do I find the missing constants? - I’m Not Feeling Like Evaluating Constants, Thanks

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Hotplates

“Do the hotplates heat the food through properly?” “Oh yes, they come out of the oven at 200 degrees and the temperature drops by a degree every minute.” To @dragondodo’s credit, she did not launch into a lecture on Newton cooling. But she did grumble about it to me -

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Ask Uncle Colin: A Partition Enigma

Dear Uncle Colin, In reading Sir Dermot Turing’s XY&Z, he states that the number of species of cycle is 101 - and after a bit of thought, I figured out that that’s the number of partitions of the number 13. However, I couldn’t work out how to get 101! Can

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The Mathematical Ninja and the *Other* Pole

“Sensei, why have you covered the entire Earth in an area-preserving wrap?” “It’s all @colinthemathmo's doing.” “I’m surprised you’re doing it in hardware rather than working it out in your head.” “Oh, $\frac{1000}{\sqrt{\pi}}$? That’s trivial.” “But of course it is.” “I mean, $\frac{1}{\pi}$ is pretty close to $\frac{1}{\sqrt{10}}$, which is

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Ask Uncle Colin: Family

Dear Uncle Colin, I have a probability question that involves a weird place where every family has three children, and every child is either a girl or a boy. 50-50. Independent of each other. If I take a random family, and choose at random one of the children, I have

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Dictionary of Mathematical Eponymy: Johnson Solids

I am a big fan of polyhedra. I’ve raved elsewhere about the icosidodecahedron, and even something as dull as a cube is something I can get behind. And so, naturally, I wondered: is there a periodic table of polyhedra? And the answer is “not exactly”. But there’s something pretty close

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Ask Uncle Colin: The Timeless SUVAT Equation

Dear Uncle Colin, I can derive the timeless SUVAT equation $v^2 = u^2 + 2as$, but I can’t intuitively see where it comes from. Any clues? - Everyone Needs Explanations, Really Get Yours Hi, ENERGY, and thanks for your message! This is one that I never really picked up on

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Revisiting Minesweeper

Many moons ago, I looked into the game theory of Minesweeper, and - in particular, what you should do in this situation: I think I got my probabilities wrong there, and want to put that right. If you want to work out the correct move (and associated probabilities), you should

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Ask Uncle Colin: A Parametric Integration

Dear Uncle Colin, I have the parametric equations $x = (t+1)^2$ and $y = \frac{1}{2}t^3 + 3$ and the lines $y = 16 - x$ and $x=1$. I need to find the area enclosed by the curve, these two lines and the $x$-axis, but my answer doesn’t agree with the

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Calculating $e^e$ and $e^{-\frac{1}{e}}$

"The Mathematical Ninja is currently on sabbatical. Leave a message after the tone... or else!" Oh dear! How are we going to figure out $e^e$ now? Let alone $e^{-\frac{1}{e}}$? We'll just have to roll up our sleeves and get our thinking hats on, that's all. OK, $e^e$ First of all,

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