How does the shape of the earth affect how far you can see?

Assume you are on the ocean so no other features can obstruct your view. As you look at the horizon, the remainder of that view is below the horizon because of the curvature of the earth. Pick up any ball. Hold it at eye level & place your other hand on the other side of the ball. You cannot see the other hand beacause it is hidden behind the curvature of the ball.

If the degree of curvature is less, you will see a longer distance. Take a plastic flexible ruler and try it. I've not try it but such an example just came to my mind.

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