- earth is flat
- earth is round
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Skipping over what should be an extremely easy question - where is the edge? - that you have not once even attempted to answer, I will bring up another one
If the Earth is a flat circle as claimed, explain the patterns of the sun and night and day. You say we should do our own research, so give this a try. Find a flat circular object and some small object to represent the sun, and try to find a place where it is visible from one area of the circle without being visible to any other.
The only way that patterns of night and day and seasonal changes can work is with a slightly oblong sphere rotating on a tilted axis
Best argument that I have is with a little trigonometry you can easily and quickly figure out the curvature of the earth.
Direct TV satellite positions are published, and instructions on how to direct your antenna are on its website. So you can figure out exact distance between locations on the earth by simple high school math and compare to Google maps to figure out exact curvature and land distance. As this information is both utilitarian and not government it would be hard to argue against the accuracy of the test.