Image credit: The Flat Earth Society.
Here is an easy, straightforward method for proving that flat Earthers are incorrect about the geometry of the Earth. Supplies: a computer connected to the Internet, paper and pencil. Prerequisites: some basic skills with math and Internet research.
Earth maps, flat and spheroid alike, can be used to produce predictions about minimum flight times. The fastest way to travel from one place to another is in a straight line. By flying in a straight line, a plane can fly from one place to another in the shortest amount of time possible for its speed.
If you believe, for example, that a given flight from New York City to Paris is traveling no faster than 600 miles per hour, then a spheroid Earth model tells you that the minimum flight time is approximately 6 hours (based on a distance of 3,627 miles). The calculation is to divide the distance by the speed.
Any adequately labeled flat Earth map should enable you to measure the approximate distances between major cities. If you have a flat Earth map displayed on the computer screen, and it has a legend marking out the distances, then you can use that legend to improvise a ruler by holding up paper next to the legend and using a pencil to mark points on the edge of the paper.
A flat Earth model, compared to a spheroid Earth model, will specify different distances between cities in many cases. I conjecture that this is mathematically inevitable. Those distances can be used to estimate minimum flight times between cities. If in any single instance, a plane’s actual flight time was less than the minimum flight time at its maximum speed, as predicted by a flat Earth model, then that example falsifies that flat Earth model.
Note: In reality planes fly in three-dimensional arcs where they ascend and descend, and those arcs are longer than a straight line drawn on the surface of a flat or spheroid Earth. We will ignore this fact for the purposes of this analysis. This simplification does not undermine the integrity of the argument, because it will result in minimum flight time estimates which are lower than the actual minimum flight times. If you underestimate the minimum time for a flight according to a flat Earth model, and you show that the actual time of the flight was less than the estimated minimum, then you’ve falsified that flat Earth model.
Because the Earth is in fact a spheroid, I conjecture that for any labeled flat Earth map, you can find examples where its estimated minimum flight times between cities are greater than actual flight times for some flights, or that if that isn’t true (say because the map was specially concocted to make it false), then some other contradiction between the map’s predictions and reality can be found. My confidence is very high that this conjecture is true. I have found that my conjecture is true in the case of a single flat Earth map which I checked in this way.
I invite you to try this test using whatever adequately labeled flat Earth map is easiest at hand, and using whatever cities you want. Pick some cities, and research flights between pairs of cities, recording their estimated and/or actual flight times. Compare those numbers to the estimated minimum flight times according to the flat Earth model. You can produce those estimates by using the flat Earth model to measure the straight line distance between your two cities, and then dividing that number by some estimate of the maximum speed of the flight. 600mph is a reasonable maximum speed estimate for commercial flights, to the best of my knowledge, and you can calibrate your estimate against actual flight speeds you can research on the Internet.
If you try several pairs of cities, I fully expect you to come across a pair where the estimated minimum flight time on the flat Earth model is greater than the actual reported time of some flight. A single example like that, if the numbers are accurate, proves that that flat Earth model is false. With nothing but a computer and pencil and paper, you can try this test as much as you want, with as many flights and flat Earth maps as you want, and prove to your satisfaction that the Earth is not flat.
If you are able, it could be wonderful to go to Lake Michigan or another large lake. From the Michigan side of Lake Michigan, you would be able to see Chicago with a telescope, if the Earth were flat. Because the Earth is not flat, and is in fact a spheroid, you can’t see Chicago from across Lake Michigan. From the Michigan side, the curvature of the Earth makes Lake Michigan bulge up and cover the tops of the skyscrapers in Chicago. However, sometimes there are mirages of the Chicago skyline which can be seen from the Michigan side; these can be explained while still assuming the Earth is round. You can verify all this with Internet research, or you could go to Lake Michigan yourself to check the facts.