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"Lion Hunting"
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A contribution to the mathematical theory of big game hunting...
The following represents several mathematical methods for
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 "Mangentheoretisch" method.
We observe that the desert is a separate space. It therefore
contains an enumerable dense set if points, from which can be
extracted a sequence having the lion as a limit. We then
approach the lion stealthily along the sequence, bearing with us
suitable equipment.
* The Peano method.
Construct, by standard methods, a continuous curve passing
through point of the desert. It has been shown that it is
possible to traverse such a 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/(2 * pi * i) integral over C of [f(z) / (z - X)] dz
where C is the boundary of the desert, its value is f(X), i.e., a
lion in the cage.
* The Wiener Tauberian method.
We procure a tame lion, LO of class L(-infinity, +infinity),
whose Fouries transform nowhere vanishes, and release it in the
desert. LO 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 LO about the desert.
* The Schrodinger method.
At any given moment, there is a positive probability that
there is a lion in the cage. Sit down and wait.
* A relativistic method.
We distribute about the desert lion bait containing large
portions of the companion 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], 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.