Their Flat Earth Theory goes back to a book written in 1881 by a nuthead called Samuel Birley Rowbotham. The theory seems to be is based on two arguments :
- Looks flat to me.
- Samuel Birley Rowbotham said so.
In a nutshell, they believe the earth is a disc with the center at the north pole and surrounded by an ice wall, the sun and the moon rotate above the equator in an altitude of 3000 miles, and gravity comes from the earth accelerating constantly upwards. Oh, yes: Of course there is also a global conspiracy to hide all this, led by NASA. And the ice wall is guarded by armed guards (no, they are not called "Night Watch"). Every evidence against Flat Earth Theory is interpreted as forgery and thus taken as evidence for the conspiracy, or explained away with "bendy light". It's hilarious.
Luckily, there are some "round-earthers" arguing with these nutheads. As for me, I recently posted some arguments for round earth in their forum (my pseudonym is "Zogg"). For example, I proved that according to their numbers, sunset should happen about 26° above the horizon. They explained it away with "bendy light" and even claimed that "trigonometry is based on aggressively globularist Round Earth Theory". I laughed my a** off.
But I warn you: Whereas it's easy to find arguments why earth is not flat, I found it impossible to convince Flatearthers of the validity of these arguments. Nevertheless it's an amusing exercise.