User:Gracefool/Mathematical theory of hunting

The mathematical theory of hunting presents a number of alternative methods of hunting.

The example is of capturing a lion in the middle of the Sahara Desert.

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.

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.

The "Mengentheoretisch" 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 a limit. We then approach the lion stealthily along this sequence, bearing with us suitable equipment.

The Peano method

Construct, by standard methods, a continuous curve passing through every point of the desert. It has been shown 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.

A topological method

We observe that a 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.

The Cauchy, or function theoretical, method

We consider an analytic lion-valued function f(z). Let X be the cage. Consider the integral:

                   1        |\ C
              ------------  |
              (2 * pi * i) \| [f(z) / (z - X)]dz

where C is the boundary of the desert; it's value is f(X), i.e., a lion in the cage.

The Wiener Tauberian method

We procure a tame lion, L0 of class L(-infinity, +infinity), whose Fourier transform nowhere vanishes, and release it in the desert. L0 then converges to our cage. By Wiener's General Tauberian Theorem, any other lion, L (say), will then converge to the same cage. Alternatively, we can approximate arbitrarily closely to L by translating L0 about the desert.

The Schrödinger method

At any given moment there is a positive probability that there is a lion in the cage. We sit down and wait.

A relativistic method

We distribute about the desert lion bait containing large portions of the Companion of Sirius. When enough bait has been taken, we project a beam of light across the desert. This will bend right around the lion, who will then become so dizzy that he can be approached with impunity.

The thermodynamical method

We construct a semi-permeable membrane, permeable to everything except lions, and sweep it across the desert.

The magneto-optical method

We plant a large lenticular bed of catnip (Nepeta cataria), whose axis lies along the direction of the horizontal component as the earth's magnetic field, and place a cage at one of its foci. We distribute over the desert large quantities of magnetized spinach (Spinacia oleracea), which, as is well known, has a high ferric content. The spinach is eaten by the herbivorous denizens of the desert, which are in turn eaten by lions. The lions are then oriented parallel to the earth's magnetic field, and the resulting beam of lions is focused by the catnip upon the cage.