March, 2019

Ask Uncle Colin: Traffic Flow

Dear Uncle Colin, I read that when cars are driving at 70mph on the motorway, they take up more space than when they travel more slowly (because you need to leave a longer safe gap between them). What’s the most efficient speed for motorway travel if you want to get

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The Mathematical Ninja and the Ninety-Sevenths

“A ninety-seventh.” The student scratched her head. “I’d call that 0.01.” A moment more’s thought. “0.0103? Probably good enough.” For the Mathematical Ninja, this was about as good as could be expected. They sighed all the same and wrote down: $0. \dot 01\, 03\, 09\, 27\, 83\, 50\, 51 \\

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Wrong, But Useful: Episode 65

In this month’s Wrong, But Useful, we’re joined by @televisionduck, who is TD Dang in real life. We discuss: Chalkdust Issue 091 Fun spring cover with Harris spiral, Horoscope is back!, New academic webpage checklist (c.f. Colin’s old webpage, @standupmaths interview, top ten regulars, etc. Write for them! Talkdust, second

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Ask Uncle Colin: A Fishy Derivative

Dear Uncle Colin, I have the equation of a curve, $\frac{2x+3y}{x^2 + y^2} = 9$. If I differentiate implicitly using the quotient rule, I get $\diff{y}{x} = \frac{2(x^2 + 3xy - y^2)}{3x^2 - 4xy - 3y^2}$. If I rearrange first to make it $2x + 3y = 9\left(x^2 + y^2\right)$,

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Powers

“Here’s a quick one,” suggested a fellow tutor. “Prove that $2^{50} < 3^{33}$.” Easy, I thought: but I knew better than to say it aloud. First approach “I know that $9 > 8$,” I said, checking on my fingers. “So if $2^3 < 3^2$, then $2^{150} < 3^{100}$ and $2^{50}

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Ask Uncle Colin: Are these fractions equivalent?

Dear Uncle Colin, How can I tell whether $\frac{221}{391}$ and $\frac{403}{713}$ are equivalent? - Calculator Answer Not Considered Enough, LOL Hi, CANCEL, and thanks for your message! There’s a naive way to do it and a clever way. Let’s do it naively The naive way is to see whether $\frac{221}{391}

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A Puzzle From The MathsJam Shout (With Generating Functions)

In a recent MathsJam Shout, courtesy of Bristol MathsJam, we were given a situation, which I paraphrase: Cards bearing the letters A to E are shuffled and placed face-down on the table. You predict which of the cards bears which letter (You make all of your guesses before anything is

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Ask Uncle Colin: Solving Trigonometric Equations

Dear Uncle Colin, I’m trying to solve $2\cos(3x) = -\sqrt{2}$, for $0 \leq x \lt 2\pi$, but the answers I find are outside the specified interval, and obviously I miss the ones that are in the interval. How would you tackle this? - Like A Puzzle, Like A Cosine Equation

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Dictionary of Mathematical Eponymy: The Collatz Conjecture

What it is Every so often, one comes across a teacher who is Properly Evil. I’ll spare names here, but I have a clear, strong memory of being introduced to the Collatz conjecture on a school trip. “Take a number, let’s say 3. If it’s odd, you treble it and

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I teach in my home in Abbotsbury Road, Weymouth.

It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby.

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