If the earth is flat, it should be easy to make an undistorted map on a flat sheet of paper where the distances between cities and continents are correct, continents are all properly sized with respect to each other, and the scale is constant throughout.
Over the decades (long before sputnik, before NASA) surveyors and cartographers set out to measure and make maps, using whatever instruments they had. But the maps they came up with were distorted -- they never came up with an undistorted flat earth map.
What are the possible reasons no one has made such a map?
Here are two possibilities I can think of. I would like to know from anyone on this forum of any other possibilities anyone would like to present.
Possibility 1: There is no undistorted flat earth map on a flat sheet of paper because it's impossible if the surface you are mapping is not flat.
Possibility 2: The surveyors and cartographers measurements indeed were compatible with the earth being flat, but they were part of a vast conspiracy to purposely distort their results to make their maps appear as if the earth is not flat.
What other possibilities are there that I might have overlooked?
And also, for the second possibility -- what would have been the motivation to purposely deceive people into thinking the earth is round?