the center of the world (was Re: Check out O'Reilly's Open Source Convention Highlights)
Toby Dickenson
tdickenson at devmail.geminidataloggers.co.uk
Mon Jul 2 08:25:54 EDT 2001
"Alex Martelli" <aleaxit at yahoo.com> wrote:
>"Konrad Hinsen" <hinsen at cnrs-orleans.fr> wrote in message
>news:m33d8j8j2j.fsf at chinon.cnrs-orleans.fr...
>> markus at kepler.ibp.de writes:
>>
>> > Then find first the weighted average as a point in three-dimensional
>> > space, i.e. as (an approximation to) the center of gravity of the
>> > human population. This will be some point deep in the interior of the
>> > Earth, which you could the project back to the surface.
>>
>> But that doesn't minimize the distance on the surface.
>
>Doesn't it (in terms of great-circle distance)? I can't prove
>it in my head either way, but trying to visualize a few cases
>does suggest the requested surfacepoint IS obtained this way.
Imagine 51 people gathered at the north pole, and 50 people gathered a
very small distance away from the south pole.
Surface-distance-wise the midpoint is roughly on the equator (actually
1% of the half-circumference north of the equator)
However, the center of mass of the people lies only slightly lies off
the polar axis, but northwards of the earths center by a 1% of its
diameter. Projected onto the surface this is a point very close to the
north pole.
Best effort ascii-art:
* is the earths center
. is center of mass of people
x is that point projected onto the surface
/ \
/ \
x )
( . ) 50
N 51 ( * ) S
( )
Toby Dickenson
tdickenson at geminidataloggers.com
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