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Originally Posted by Daniel_
The point is, if we follow your prescription, there is a point at which we are hight enought to see the full circle of the world.
At zero altitude, the horizon looks like a perfect plane.
At infinite altitude (say, for example, from the Moon) the horizon is clearly circular, as one can view the entire hemisphere.
There must be some transition zone. I have seen the curvature of the earth from airliners (very high), light aircraft (moderately high) Mount St Hellens (pretty high), and the French alps (fairly high).
I have not seen it from the hills near my house, or the beach.
This would make me think that the transition zone lies between 1,000 and 6,000 feet altitude.
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I thought everyone was saying that they could see the Earth curving downward, not around, my mistake. My demonstrations just states that mathematically there is no transition, the horizon is always circular. For reference, the altitude when the world takes up your full field of vision when looking straight down at the Earth occurs roughly at 986km (613 miles), and that can be calculated with a simple formula:
{Altitude} = {radius of Earth, 6378km} * [csc({span of vision, 120 o}/2) - 1]
=6378km * (1/sin(60 o) - 1) = 986km
There are geometric formulas which are not difficult but are tedious to apply that would describe the deviation from straightness of an arc.