Where is the geographical center of all land-areas located?
Algorithm and data
This theory appeared to be based on plane geometrics: They used for example, a special map-projection type for this calculation.
However, the correct calculation can only be achieved over great-circle distances on the sphere.
This trigonometric can be done with a simple algorithm as follows. For each point on Earth, the great-circle distance to all other raster-points in the map is measured and added. This sum is displayed as a color on the following map. Blue is selected for small distance-sums:
The center: 37.688 N, 35.438 E (the historic place Iskenderun)
Pixel-Coordinates: 383x, 93y (from upper left).
The Great Pyramid: 30N, 31E.
Maybe a calculation with a better map moves the center 500km south, towards the Pyramid. But Iskenderun as center is not less interesting ;-)
The result projected on a 3D-Globe (VRML)
The geographic center is the point or the point set, which sum of all distances to all other points of the area has a minimum. On Earth surface, this distance is the arc length along the spherical great-circle between two points.
My algorithm: C-Program
As data source for the calculation, I used the NOAA 2-min digital elevation modell (DEM):
The same calculation with a map of 4000x2000 pixel resolution, does not change the result very much. So this is neither a proof for the center-theory nor a proof against it. The calculated center is in relation to the length of the equator only about 1% away from the Great Pyramid, which speaks more pro the center-theory than against it!
The algorithm and some test-data