>>12970204>stand on a mountain >can't see any curvatureYou see the curvature by measuring how far you can see, the law being that your visibility radius is the square-root of twice your height times the radius of the Earth, about 5km for a 2m person (square root of 2 times 6000km times 2m).
This handy formula shows you that if you have a crow's nest which is 20 meters above the ground, you can see 3.16 times further, the square root of 10, about 15 km. If you want to see 50km, you need to be 200 meters up, so forget about it. When you are 10 km above the ground, you can see 240km out, this is an airplane's cruising height.
The formula comes from the law of a sphere, a sphere looks like a parabola near the to
This is true for small x, it's the leading Taylor expansion of square-root. You can see as far as when the slope from your eye is tangent to the parabola. Extrapolating the tangent of a parabola from position x, the slope is x/R, this is the derivative, and it's a distance x, so it's x^2/R in height for the line, but you are starting x^2/2R below ground level, so the extra height for the tangent is x^2/2R
Where h is how far up your vantage point is.
The law is very easy to check today, and it can be done by anyone from a local mountain.
