Kek!
(media.conspiracies.win)
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4th grade math-
"The Earth's radius (r) is 6371 km or 3959 miles, which gives a circumference (c)of c = 2 * π * r = 40 030 km
We wish to find the height (h) which is the drop in curvature over the distance (d)
Using the circumference we find that 1 kilometer has the angle 360° / 40 030 km = 0.009°. The angle (a) is then a = 0.009° * distance (d)
The derived formula h = r * (1 - cos a) is accurate for any distance (d)
I don't have time to bother with Archimedes.
Adult math: Earth round. 360°. 1°=60 nautical miles. 360 x 60 = distance around earth north to south and back. Standard set on latitude scale. Convert to stupid math to get KM.