Ali’s blog

Mostly quant stuff with occasional digressions

How to catch a lion in the desert

Posted by alifinmath on February 15, 2008

I first read this in a British mathematics magazine in 1987. It’s available online, and I’m pasting some of the more ingenious mathematical methods for catching a lion:

1.2 The method of inversive geometry

We place a spherical cage in the desert, enter it and lock it. We perform an inversion with respect to the cage. The lion is then in the interior of the cage, and we are outside.

1.3 The method of projective geometry

Without loss of generality, we may regard the Sahara Desert as a plane. Project the plane into a line, and then project the line into an interior point of the cage. The lion is projected into the same point.

1.4 The Bolzano-Weierstrass method

Bisect the desert by a line running N-S. The lion is either in the E portion or in the W portion; let us suppose him to be in the W portion. Bisect this portion by a line running E-W. The lion is either in the N portion or in the S portion; let us suppose him to be in the N portion. We continue this process indefinitely, constructing a sufficiently strong fence about the chosen portion at each step. The diameter of the chosen portions approaches zero, so that the lion is ultimately surrounded by a fence of arbitrarily small diameter.

1.5 The ‘Mengentheoretisch’ [set-theoretical] method

We observe that the desert is a separable space. It therefore contains an enumerable dense set of points, from which can be extracted a sequence having the lion as limit. We then approach the lion stealthily along this sequence, bearing with us suitable equipment.

1.6 The Peano method

Construct, by standard methods, a continuous curve passing through every point of the desert. It has been remarked that it is possible to traverse such a curve in an arbitrarily short time. Armed with a spear, we traverse the curve in a time shorter than that in which a lion can move his own length.

1.7 A topological method

We observe that the lion has at least the connectivity of the torus. We transport the desert into four-space. It is then possible to carry out such a deformation that the lion can be returned to three-space in a knotted condition. He is then helpless.

1.8 The Cauchy, or function-theoretical, method

We consider an analytic lion-valued function f(z). Let zeta be the cage. Consider the integral is the boundary of the desert http://users.ox.ac.uk/~invar/integral.gif; its value is f(zeta), i.e., a lion in the cage.

The stochastic method for catching a lion can be found here.

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