Posted in dome

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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Posted in ask uncle colin

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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Posted in game theory

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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Posted in ask uncle colin

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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Posted in ninja maths

"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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Posted in podcasts

In the 71st episode of Wrong, But Useful, we’re joined by @nookiedv, who is Anouk de Vos in real life. We discuss: Number of the podcast: 1729, a fairly uninteresting number. Sums of cubes updates: 33 42 3 is also interesting as there are two solutions but it’s unknown if

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Posted in ask uncle colin

Dear Uncle Colin, I just solved $2\cos^2(4x)=1$ between 0 and $2\pi$ and found four solutions: $\frac{1}{16}\pi$, $\frac{3}{16}\pi$, $\frac{5}{16}\pi$ and $\frac{7}{16}\pi$. The answer scheme says there are sixteen solutions! Where have I gone wrong? Have You Perhaps A Trig Identity Answer? Hi, HYPATIA, and thanks for your message! Looking at your

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Posted in Uncategorized

A puzzle via @CmonMattTHINK (Matt Enlow): There is a line that is tangent to the curve y = x^4 - x^3 at two distinct points. What is its equation? (Can you find it without calculus?) #iteachmath #math #maths #mathchat #mathschat — Matt Enlow (@CmonMattTHINK) December 21, 2018 (I think we

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Posted in ask uncle colin

Dear Uncle Colin, I have a little problem. You see, there’s this bird, A, in its nest at time $t=0$ - the nest is at $(20, -17)$ - and it travels with a velocity of $-6\bi + 7\bj$ (in the appropriate units). But there’s another bird, B, whose nest is

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Posted in number theory

My cunning plan, back last August, was sadly foiled: @christianp refused to rise to the bait. I'd written a post about finding the smallest number such that moving its final digit to the front of the number doubles its value. It turned out, to my surprise, to be 17 digits

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