Posted in calculus, integration

What is the volume above a plane, and inside a sphere of radius $r$, such that the radius of the circle where the two intersect is $R \sin(\alpha)$? What is this spherical sector's curved surface area? I've lost the precise wording of the question that drove a small cabal of

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Posted in ask uncle colin, geometry

Dear Uncle Colin, I'm trying to sew a traditional football in the form of a truncated icosahedron. If I want a radius of 15cm, how big do the polygons need to be? -- Plugging In Euler Characteristic's Excessive Hello, PIECE, and thank you for your message! Getting an exact answer

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Posted in ninja maths, statistics

"What are the ch..." "About 11.7%," said the Mathematical Ninja. "Assuming $X$ is drawn from a Poisson distribution with a mean of 9 and we want the probability that $X=7$." "That's a fair assumption, sensei," pointed out the student, "given that that's what the sodding question says." A wiser student

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Posted in ask uncle colin, calculus, core 4

Dear Uncle Colin, I have a pair of parametric equations giving $x$ and $y$ each as a function of $t$. I'm happy with the first derivative being $\diff{y}{t} \div \diff{x}{t}$, but I struggle to find the second derivative. How would I do that? - Can't Handle An Infinitesimal Nuance Hi,

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Posted in ask uncle colin

Eagle-eyed friend of the blog @robjlow spotted an error in Uncle Colin's last answer. As I'm forever telling my students, making errors is how you learn; Rob has graciously delivered a lesson for us all. Thanks for keeping me honest! Recently, Uncle Colin gave a couple of ways to see

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Posted in ask uncle colin

Dear Uncle Colin, What is $\lim_{x \to \infty} \left\{ \sqrt{x^2 + 3x} - x\right\}$? - Raging Over Obnoxious Terseness Hi, ROOT, and thanks for your very brief question. My approach would be to split up the square root and use either a binomial expansion or completing the square, as follows:

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Posted in podcasts

In this month's installment of Wrong, But Useful, our special guest co-host is @mathsjem (Jo Morgan in real life) from the indispensable resourceaholic.com. We start by talking about resourceaholic.com and how Jo manages to fit such a punishing blog schedule around being a nearly-full-time maths teacher. Colin wonders how writing

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Posted in calculus, pirate maths

"Arr, that be a scurvy-lookin' expression!" said the Mathematical Pirate. "A quartic on the top and a quadratic on the bottom. That Ninja would probably try to factorise and do it all elegant-like." "Is that not the point?" "When you got something as 'orrible as that, it's like puttin' lipstick

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Posted in ask uncle colin, ninja maths

Dear Uncle Colin, Help! My calculator is broken and I need to solve - or at least approximate - $0.1 = \frac{x}{e^x - 1}$! How would you do it? -- Every $x$ Produces Outrageous Numbers, Exploring New Techniques Hi, ExPONENT, and thanks for your message! That's a bit of a

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Posted in arithmetic, ninja maths

"Sensei! I have a problem!" The Mathematical Ninja nodded. "Bring it on." "There's a challenge! Someone has picked a five-digit integer and cubed it to get 6,996,364,932,376. I know it ends with a six, and I could probably get the penultimate digit with a bit of work... I just wondered

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