November, 2013

How the gravitational slingshot works

The gravitational slingshot is something I'd heard about but had never bothered to look up - until now. It sounded like magic: you fire a spaceship towards a planet and (then a miracle occurs before) it comes out moving faster. It's how the Voyager spacecraft picked up enough speed to

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How I factorise quadratics these days

It's nearly two years since I last tackled quadratics with a number in front. Recently, though, I stumbled on a slightly different method that's a bit less involved. I won't say it's easier or better - different methods suit different people, after all - but I like it. Let's factorise

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A student asks… about the Simplex Algorithm

A student asks: I'm struggling with the simplex algorithm. How do I read the tableau at the end? And how do I pick the right pivot? The simplex algorithm - which is D2 for most students, but D1 if you're doing OCR - is frequently listed as one of the

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Tactical preference voting

One of the OTHER things I love about MathsJam is that I always come away with a notebook full of new ideas for posts. Most of them are indecipherable, but some stick in the mind. This one is based on a real-life dilemma posed by a friend of Elizabeth, which

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Escoffier, Joyce and Einstein

In complaining that astrophysics was hard because of all the maths, a student recently told me: "The way it's presented is: 'OK, you get that $A+B=C$? Excellent. Now derive $DQH$, use a matrix to get $Y$, find $M$ by mysterious means. What? Why can't you do that?" Let's start with

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Exact trig values – Secrets of the Mathematical Ninja

The Mathematical Ninja surreptitiously pressed a button under the table. There was a flash, a sizzle and a slight smell of burning. The student prodded the on-button of his calculator increasingly frantically. "Oh dear," said the Mathematical Ninja. "It must have been a passing electromagnetic storm that's permanently fried the

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Why I loved the MathsJam conference

Because, well, what's not to love? About 100 mathematicians gathered together to play with maths for a whole weekend. What, in all seriousness, could be better? There's something fantastic about there being, in one room, probably about as much mathematical brainpower as the Manhattan Project, and for all of that

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Heroic triangles

In a recent Maths Challenge, students were told the area of a triangle ($7$cm$^2$) and the length of two of its sides ($6$cm and $8$cm), and asked how many possible lengths there were for the third side. It's easy enough to show there are two: let the base of the

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