How as an individual can I know if the Earth is a sphere or a flat disc? What experiment can I do that doesn't involve trusting information from a 3rd party that would prove what the geometry really is?
Look at the angle of the sun at noon at a certain point in time, and then come to another point (preferably of the same latitude), for a large number of kilometers. Then again look at the angle of the sun and calculate the difference. Multiply the distance between these points by 360 and divide by the amount that we got when weaned. Thus, they proved that the earth is round 2.5 thousand years ago.
There are also a lot of experiments with magnetic coils that interact with the magnetic field of the earth, they very clearly show the fact that we are not perpendicular to the magnetic field (Otherwise, we could create transport on the magnetic field of the earth)