🚀 go-pugleaf

mjfreem@hubcap.clemson.edu (Matthew J. Freeman) writes:
> isaak@aurora.com (Mark Isaak) writes:
> >Four points are randomly selected from the surface of a sphere.
> >What is the probability that all four lie in the same hemisphere?
> >How about for 5 points?  6?  more?
> 
> Think of placing 4 points on an otherwise featureless sphere.
> The first three points will define a hemisphere no matter
> where they are placed, ...        ^^^
                                     |
Really?  For example, Rome, Berlin, and Prague are all on the northern
hemisphere --- but surely they are as well not much east of Greenwich,
so there's another hemisphere --- the one with the border through Greenwich
and the North Pole.  On the other hand, not all hemispheres are equally
likely to contain these three points and the likeliness changes drastically
if the points are far away!

It seems that one has to look on the distances between points...

ralf
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