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Rule collision
The same experience has happened to me several times in the Maths Drop-In Centre recently – with different students from different courses – and it was such a strong pattern I need to talk about it.
The students are doing some algebra involving negative powers on the tops of fractions. Something like this:
Rapunzel's Epiphany
We bought Disney Studio's newest film "Tangled" on the weekend and I have to say it's one of my favourite movies ever. It's certainly Disney's best movie since "Beauty and the Beast", and I dearly loved "Beauty and the Beast". I should warn you now that in order to say what I want to say I'm going to have to reveal a bit of the plot, so let this count as your spoiler alert.
Not quite the bisection method
In various first year maths courses here, the students learn the "bisection method" for finding zeros of continuous functions. (A zero of a function is a number that makes the answer of the function come out to zero – it's therefore also a point where the graph of the function crosses the x-axis.) It's based on the Intermediate Value Theorem, which basically says that if the function is below zero at one spot and above zero at another, then is must be equal to zero somewhere in between. Here's how the process goes:
