2 thoughts on “Mathematics of Lion Catching

  1. Something of a non sequitur, but this reminds me of my first real analysis course. The lecturer (Professor Tom Korner) had a favourite technique, which he called lion hunting. It worked as follows:

    You have an interval [a_0, b_0]. You want to find some point x somewhere in this interval. So, you divide the interval into two subintervals, [a_0, c_0] and [c_0, b_0] (usually c_0 = (a_0 + b_0)/2 ) and determine which of these subintervals x lies in. If it’s int he left, you let a_1 = a_0, b_1 = c_0, if it’s in the right you do similarly. You repeat this process, and the a_n and b_n both tend to a common point which is your desired x.

    The reason it’s called lion hunting is that the intuitino is you’ve got a lion somewhere in the interval (jungle), and you want to find it. So you stick a net across the jungle and wait till you hear signs of a lion on one side of the net. So now you want to narrow down where the lion is within that part of the jungle…

    Anyway, this turns out to be a surprisingly good way to introduce a lot of real analysis, because it basically boils down to doing a binary search for the solution, which is a very intuitive approach to problem solving.

    So, want to prove the intermediate value theorem? Do it by lion hunting! Start with f : [a, b] -> R with f(a) = f(a_n) -> f(x) and 0 f(x), so f(x) = 0.

    You can also use it to prove bolzano weierstrass. You choose one of the intervals which contains infinitely many terms of the sequence, get x and from the construction there’s a subsequence tending to x.

  2. Hmm. Something got mangled in the course of editing my explanation of the proof of the intermediate value theorem via lion hunting. I’m sure it’s obvious what I really meant to write anyway. :-)

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