The following is from a book whose title I don't recall. The book is in German, but the article is actually a translation from the original by H. Perard, which appeared in the American Monthly 54, 466 (1938).

A CONTRIBUTION TO THE MATHEMATICAL THEORY OF BIG GAME HUNTING

Problem: To catch a lion in the Sahara Desert.

1.           Mathematical Methods

1.1           The Hilbert (axiomatic) method

We place a locked cage onto a given point in the desert. After that, we introduce the following logical system:

          Axiom 1: The set of lions in the Sahara is not empty.
          Axiom 2: If there exists a lion in the Sahara, then there exists a lion in the cage.
          Procedure: If P is a theorem, and if the following holds: "P Q," then Q is a theorem.
          Theorem 1: There exists a lion in the cage.

1.2          The geometrical inversion method

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

1.3          The projective geometry method

Without loss of generality, we can view the desert as a plane surface. We project the surface onto a line and, afterwards, the line onto an interior point of the cage. Thereby the lion is mapped onto that same point.

1.4          The Bolzano-Weierstrass method

Divide the desert by a line running north to south. The lion is then either in the eastern or western part. Let's assume it is in the western part. Divide this part by a line running east to west. The lion is either in the northern or southern part. Let's assume it is in the northern part. We can continue this process arbitrarily and thereby construct with each step an increasingly narrow fence around the selected area. The diameter of the chosen partitions converges to zero so that the lion is caged into a fence of arbitrarily small diameter.

1.5          The set theoretical method

We observe that the desert is a separable space. It therefore contains an enumerable dense set of points that constitutes a sequence with the lion as its limit. We silently approach the lion in this sequence, carrying the proper equipment with us.

1.6          The Peano method

In the usual way, construct a curve containing every point in the desert. It has been proven [1] that such a curve can be traversed in arbitrarily short time. Now we traverse the curve, carrying a spear, in a time less than it takes the lion to move a distance equal to its own length.

1.7          A topological method

We observe that the lion possesses the topological gender of a torus. We embed the desert in a four dimensional space. Then it is possible to apply a deformation [2] of such a kind that the lion, when returning to the three dimensional space, is all tied up in itself. It is then completely helpless.

1.8          The Cauchy method

We examine a lion-valued function f(z). Let be the cage. Consider the integral
func{ 1/(2 pi iota) INT from C {{f(z)} over {z~-~ zeta }dz} }where C represents the boundary of the desert. Its value is f( }, i.e., there is a lion in the cage [3].

1.9          The Wiener-Tauber method

We obtain a tame lion, L0, from the class L(-infinity,infinity), whose fourier transform vanishes nowhere. We put this lion somewhere in the desert. L0 then converges toward our cage. According to the Wiener-Tauner theorem [4] every other lion L will converge toward the same cage. (Alternately, we can approximate L arbitrarily close by translating L0 though the desert. [5])

2          Theoretical Physics Methods

2.1          The Dirac method

We assert that wild lions can ipso facto not be observed in the Sahara Desert. Therefore, if there are any lions at all in the desert, they are tame. We leave catching a tame lion as an exercise to the reader.

2.2           The Schroedinger method

At every instant there is a non-zero probability of the lion being in the cage. Sit and wait.

2.3          The nuclear physics method

Insert a tame lion into the cage and apply a Majorana exchange operator [6] on it and a wild lion.

2.4          A relativistic method

All over the desert, we distribute lion bait containing large amounts of the companion star of Sirius. After enough bait has been eaten, we send a beam of light through the desert. This will curl around the lion so it gets all confused and can be approached without danger.

3          Experimental Physics Methods

3.1          The thermodynamics method

We construct a semi-permeable membrane that lets everything but lions pass through. This we drag across the desert.

3.2          The atomic fission method

We irradiate the desert with slow neutrons. The lion becomes radioactive and starts to disintegrate. Once the disintegration process has progressed far enough, the lion will be unable to resist.

3.3          The magneto-optical method

We plant a large, lens-shaped field with catnip (nepeta cataria) such that its axis is parallel to the direction of the horizontal component of the earth's magnetic field. We put the cage in one of the field's foci. Throughout the desert we distribute large amounts of magnetized spinach (spinacia oleracea), which has, as everybody knows, a high iron content. The spinach is eaten by vegetarian desert inhabitants, which in turn are eaten by the lions. Afterward, the lions are oriented parallel to the earth's magnetic field, and the resulting lion beam is focused on the cage by the catnip lens.

NOTES

[1] After Hilbert, cf. E. W. Hobson, "The Theory of Functions of a Real Variable and the Theory of Fourier's Series" (1927), vol. 1, pp 456-457
[2] H. Seifert and W. Threlfall, "Lehrbuch der Topologie" (1934), pp 2-3
[3] According to the Picard Theorem (W. F. Osgood, "Lehrbuch der Funktionentheorie," vol 1 (1928), p 278) it is possible to catch every lion except for at most one.
[4] N. Wiener, "The Fourier Integral and Certain of Its Applications" (1933), pp 73-74
[5] N. Wiener, ibid, p 89
[6] cf e.g., H. A. Bethe and R. F. Bacher, "Reviews of Modern Physics," 8 (1946), pp82-229, esp. pp 106-107
[7] ibid pp 106-107
[8] ibid