My intention here is to undeniably prove whether the Earth is flat or not. You seem to present some book as the evidence for its flatness, but, since most people do not have access to this book, I shall demand that You present us with a map of the world or at least of the United States according to your Flat Earth Model in order to continue a more objective discussion. You should not have a problem in this quest, because, unlike the Round Earth model, the Flat Earth can always be accurately drawn on a flat surface. After all, the proponents of the Round Earth model came up with the globe as a representation of their view of the world. In fact, there is a picture of a map of some kind on this site.

But, please beware that the globe enables one to make distance calculations between any two points on it along a certain path, so your map must also have this feature. Now, calculating two arbitrary lengths in this way on the globe and comparing them with lengths measured directly on the Earth's surface for the corresponding points, we can check whether the ratios between the calculated lengths are the same as the ratios between the measured lengths. If the Flat Earth model is true, than the above ratios must be the same for any two arbitrary lengths (up to the uncertainty in measuring lengths and local variations in the model, like mountains, hills, valleys, canyons, etc.). Now, we can not check all the possible lengths on the Earth, since it would take an infinite amount of time. This statement can be effectively used to disprove the theory, since it is a necessary condition, and not a sufficient one. Indeed, making a contraposition, we can say that:

“

*If there are two lengths for which the above ratio deviates more than the experimental error would allow it, then the Flat Earth Model can not be true.*”

Now, there is not anything special about the Flat Earth model that makes the above statement true. It will be just as correct for the Round Earth Model. This is because it is a consequence of logic. What is different between the two is the way to calculate the distance along a certain path between two points on the Earth. In fact, the two models can not give equal predictions for all the paths on the Earth because this would imply that they are isometric. But, as is well known from Differential Geometry, this is not true for a spherical and a flat surface.

Also, one must be able to orient oneself on the surface of the Earth. According to the Round Earth Model, there are 3 general ways of orientation (listed in an ascending order of accuracy):

- By using the Earth Magnetic Field and the fact that the north pole of the magnetic needle always points approximately to the geographic North Pole (and the south pole to the geographic South Pole);
- By using the rotation of the Earth’s sphere around the North – South pole axis (World Axis) and the fact that every star rotates on the celestial sphere around a circle with a center pointing to the World Axis;
- By using the rotation of Earth’s sphere and a gyro – compass which aligns itself parallel to the World Axis.

There are other ways to orient oneself (GPS), but, since You say that satellites do not exist, these methods would suffice. You have to define the meaning of the cardinal directions in your model of Flat Earth.

Besides metrical inconsistencies, the two models (Flat and Round Earth) are also topologically not equivalent. This is best seen by the absence of the South Pole on the Flat Earth Model, whereas the Round Earth predicts the presence of one. I guess this situation has been chosen, because this leaves the inhabited areas on the map whereas keeping any two points on the Earth connected along the surface. This would have not happened if the Globe was cut in the Pacific Ocean and the surface developed in a plane, because it would mean that one can not go from USA to Japan by going west, for example.