Browsing category ninja maths

The Mathematical Ninja and the Cube Root of 4

The student swam away, thinking almost as hard as he was swimming. The cube root of four? The square root was easy enough, he could do that in his sleep. But the cube root? OK. Breathe. It’s between 1 and 2, obviously. What’s 1.5 cubed? The Mathematical Ninja isn’t going

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The Mathematical Ninja and the SSNs

A professor – according to Reddit – asked their class how many people you’d need to have in a room to be absolutely certain two of them would have Social Security numbers1 ending in the same four digits (in the same order). 10001, obviously. How about a probability of 99.9%?

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Using Units to Deal With Density

Glancing over sample papers for the new GCSE, I stumbled on this: Zahra mixes 150g of metal A and 150g of metal B to make 300g of an alloy. Metal A has a density of $19.3 \unit{g/cm^3}$. Metal B has a density of $8.9 \unit{g/cm^3}$. Work out the density of

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The Mathematical Ninja and $\sin(15º)$

The Mathematical Ninja sniffed. “$4\sin(15º)$? Degrees? In my classroom?” “Uh uh sorry, sensei, I mean $4\sin\br{\piby{12}}$, obviously, I was just reading from the textmmmff.” “Don’t eat it all at once. Now, $4\sin\br{\piby{12}}$ is an interesting one. You know all about Ailes’ Rectangle, of course, so you know that $\sin\br{\piby{12}}=\frac{\sqrt{6}-\sqrt{2}}{4}$, which

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The Maths Behind… Cakes

“Cooking,” said my friend Liz in a recent Facebook post, “is one of the activities where maths is most useful in my everyday life.” She added this picture: I’ve got several reasons for wanting to share this. 1. It’s pretty much a model answer Imagine you’re in a GCSE exam,

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Ask Uncle Colin: Shouldn’t this be simple?

Dear Uncle Colin, I've got a funny square and I can't find $x$. Can you help? – Oughta Be Simple, Can't Unravel Resulting Equations Hi, OBSCURE, and thanks for your message! You're right, it ought to be simple… but it turns out not to be. It is simple enough to

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The Mathematical Ninja takes a square root

"So," said the Mathematical Ninja, "we meet again." "In fairness," said the student, "this is our regularly-scheduled appointment." The Mathematical Ninja was unable to deny this. Instead, it was time for a demand: "Tell me the square root of 22." "Gosh," said the student. "Between four-and-a-half and five, definitely. 4.7

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The Mathematical Ninja and Cosines

As the student was wont to do, he idly muttered "So, that's $\cos(10º)$…" The calculator, as calculators are wont to do when the Mathematical Ninja is around, suddenly went up in smoke. "0.985," with a heavy implication of 'you don't need a calculator for that'. As the student was wont

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A common problem: not reading carefully

I'm a big advocate of error logs: notebooks in which students analyse their mistakes. I recommend a three-column approach: in the first, write the question, in the second, what went wrong, and in the last, how to do it correctly. Oddly, that's the format for this post, too. The question

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The Mathematical Ninja and the Poisson Distribution

"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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