Mathematical_Recreations-Kraitchik-2e

18 Mathematical Recreations
given legs. Whoever reaches the goal first shall be rewarded
with the largest portion of the prey."
At the signal given by the mother the eight spiders shot
out in eight different directions at a speed of 0.65 mile per
hour. At the end of 6N seconds they simultaneously converged
on the fly, but found no need of attacking it since its
heart had given way at the sight of enemies on all sides.
What are the dimensions of the room?
They have not been stated, and it does not seem clear
how to arrive at them.
5 F
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FIGURE 1. The Spiders to the Fly: 8 Paths.
In general the shortest distance between two points is
measured along the straight line joining them. If the given
distance is to be measured over a surface that is not plane,
the shortest path, called a geodesic, is not generally a straight
line. Sometimes there are many equally short paths, as in
the case of the shortest path between two poles on a sphere,
where anyone of the infinitely many meridians joining them
will serve. Thus we may expect that the problem may have
to be examined with some care when the surface is a parallelepiped.
The key to the problem is the fact that the length of a path
on a polyhedral surface is not altered when the angles at
which the plane faces intersect are changed. In particular,
if the polyhedron may be cut along certain edges in such a