Many flat guys claim the Sun produces a spotlight circle of light on the earth as it floats around.
Many flat guys bang on about how they can't make an accurate map of the world because they don't have the cash for it.
Well here's how you can utilise the first idea to help with the second... of course this will only work IF the sun really is a spotlight
What you need to do is collect data on times of sunrise and sunset for different places around the world at the same moment in time. For example, you pick a date and time - say, 8th September at 5.00pm GMT - and you find sunrise and sunset times that correspond with that moment. For example, at 5.00pm GMT the sun may be rising in Tokyo and setting in Berlin.
Get as many different locations as you can. Then draw a circle on a piece of paper and plot the points on the edges to represent sunset and sunrise. You can tell where on the circle to put the points because the latitude of the location tells you how far up or down you need to put the point. Sunrises go on the eastern edge and sunsets on the western edge. Do this for multiple times and dates, get enough points and presto! You have a rough map of the world.