Centroid of the Earth's Surface

[Muhammad Hutasuhut]

Saudi Arabia appears to be at the center (or centroid) of the earth's
dry land. I would like to prove it by using Mathematica. I need guidance
on how to do it!

Regards
M. J. Hutasuhut

[Henry Lamb]

I hate to disappoint you, but it can't be done. That's because the
earth's surface has no centroid. Only bounded surfaces (or volumes) have
centroids. If Saudi Arabia appears to be at the centre of the earth,
that's due to the map you're using. Buy a globe.

Henry Lamb

[Zakir F. Seidov]

keywords:
centroid/ dry land of Earth/ Mathematica

Hi,
I'm not sure, but it seems to me that dry land
(as well as sea/oceans) on the Earth surface
can perfectly have centroid or any other center -
depending on assumptions.
=========================

E.g. Saudia Aravia itself has a certain centroid,
and it's easily can be found,
if you draw map of S.A. on (a hard) paper,
cut it by contour,
hang it two times in two positions of nail,
and two crossing "verticals"'ll give centroid. This is trivial.

The problem arises for larger territories
when the map is NOT flat.
If the centroid is stiil defined as center of gravity,
then MATHEMATICA is OK to calculate centroid of any 3D surface,
but centroid of DRY LAND SURFACE should be somewhere deep inside,
close to Earth's center -
to bitter dissapointment of any patriot of his/her homeland.

Interestingly enough, semi-official CENTER of Euro-Asia is
somewhere in Ural mountains, in this case center being defined
as point of maximal (or minimal?) mean distance from boundaries of
Euro-Asian continent.

And it's quite may be that at some assumptions
Saudia Arabia posseses a some center of dry land surface -
don't give up, Muhammad! ;-)

Zakir

%%%%%%%%%%%%%%%%%%%
Subject: Re: Centroid of the Earth's Surface
Author: Henry Lamb <hl...@cg.NRCan.gc.ca>
Organization: Steven M. Christensen and Associates, Inc and
MathTensor, Inc.

Henry Lamb

%%%%%%%%%%%%%%%%%%%
Subject: Centroid of the Earth's Surface
Author: Muhammad Hutasuhut <mhuta...@sympatico.ca>
Organization: Steven M. Christensen and Associates, Inc and
MathTensor, Inc.

Regards
M. J. Hutasuhut
%%%%%%%%%%%%%%%%%%%%%

[Jonathan Rockmann]

Very nicely put Zakir. I think this was just a simple case of knowing what one means.

Jon
mth...@msn.com

[Ken Levasseur]

Suppose that all of the dry land on earth consisted of two disjoint, square islands of
identical area. Where would the centroid be located?

Ken Levasseur
Math. Sciences
UMass Lowell