A Fools Guide to Flat Earth

After exploring mathematically the problem with flat earth in a previous post it is much more easily seen visually.

Here again is one version of the Flat Earth: the Azimuthal projection. The thing to note in this projection is that the distance around the disk increases as you travel away from the North Pole. By the time you get to the South Pole it is more than 6x the distance from the North Pole. This is the only map with this distance property.




The Globe Earth model viewed from the South looks like this. As we move away from the Equator the distance around the globe shrinks to zero at the South Pole. This is the only map with this distance property. Unlike Flat Earth models it can only be drawn in 3D.



Distances around the globe are a copy of the North but in reverse. This is hugely different from the Azimuthal where distances around the Earth continue to increase away from the equator rather than reduce again.



The result of this divergence becomes very obvious in places like Australia.

Now look at actual distances on the maps. On the Azimuthal the distance across Australia is roughly the distance across Asia (about a little finger on my screen). On the globe the distance across Asia is more than twice the distance across Australia. There is a huge difference in distances.

As described more accurately in the previous post Google Maps uses a very simple distance estimating tool based on a globe model. I recreate it accidentally in the post. IF the world really was Azimuthal then this tool would give distances 2/3 too small in Australia which would be really noticeable. I spoke to some people who had lived in Sydney and they confirmed that the distance to Canberra is about 2 hours drive and not the 3 hours that an Azimuthal flat earth predicts.

It is fairly simple to show that the world is not Azimuthal Flat Earth. However there are an infinite number of other flat earth maps. And while each flat earth can be chosen to approximate the globe in some region, they all suffer from the same problem of huge divergence somewhere else. Given a particular Flat Earth model it is fairly trivial then to determine the region of divergence and get some simple car journey or shipping data to confirm which model is most practical.

Of course the Earth is not an exact Sphere any more than it is an exact Disk. But, approximating it to a sphere gives remarkably accurate results. I still cannot believe that Google only uses a simple Cosine Rule to estimate global distances, and that appears to be good enough across the globe. At least I've not heard people coming back from travels complaining their phones were out. This fact alone suggests the Earth really is very close to a sphere.

There was a time when we didn't travel much where a flat earth model really was good enough. But every region of the world would have its own flat earth map. To have a single model that works for all places we need to shift into 3D and have something like a global model.