[Curious Squirrel]

Been starting to read some things and it finally struck me what was bugging me with this one. Where's the right angle? If the Earth is a sphere, walking any distance away from a starting point would leave you no longer at the same level as where you started, thus no longer at a right angle to your starting point. Right? What am I missing here?

P.S. Not sure if right forums, taking a guess.

[Rounder]

You are right.  The right angle is between the vertical line joining the earth's center and the observer, and the horizontal line tangent to the surface of the earth at the observer's eye level.  The hypotenuse is the vertical line joining the earth's center and some point on the earth's surface at a distance from the observer.  The calculated difference between them is the amount of obscured height at the distant location.

[Curious Squirrel]

Ah, ok I was managing to miss the meaning of the subtraction step. Whoopsie. Corollary then, how does this equate to a 350 foot tall wall of water? Wouldn't the water follow the curve of the earth? So, if you stood on that beach, looked out along a perfectly level plane (for a perpendicular line) if it was a flat Earth, you would be looking directly at head level of the beach on the other side. If the Earth is round, you would be looking at a point, roughly 350 feet up. Right? What do you see when you do this? The notes in the wiki don't suggest he's using any kind of measuring device, instead implying this 'wall of water' that he can't see (but which shouldn't be there to begin with right?).

[Pete Svarrior]

If the Earth is round, you would be looking at a point, roughly 350 feet up. Right?

Right. But you don't. You're looking at another beach. So: either you're looking 350 feet lower than you think you are (at which point you should be looking at lotsa water), or the Earth isn't as round as you assumed.

[Rounder]

The same geometry that has you looking at a point above the earth's surface on a round earth also means that if you were attempting to look at a distant spot on the ground, you would have to be able to see throught the curved volume of water between your observing location and the target location.  That's what the "wall of water" refers to.  The "wall of water" isn't actually 350 tall, and it isn't actually a "wall".  It is a sea-level surface behind which is obscured a column of growing height as the distance increases.

[3DGeek]

Wouldn't the water follow the curve of the earth? So, if you stood on that beach, looked out along a perfectly level plane (for a perpendicular line) if it was a flat Earth, you would be looking directly at head level of the beach on the other side. If the Earth is round, you would be looking at a point, roughly 350 feet up. Right? What do you see when you do this?

What you see is exactly what you'd expect.  Here is a container ship at sea that's far enough away that the curvature of the ocean is blocking our view of the hull:

    http://upload.wikimedia.org/wikipedia/commons/e/e4/Aground_Tauranga_Pukehina_5_Oct_11_4.jpg