How many of you have sailed across an ocean before? I have. When I was approaching land, I saw it low on the horizon, and as I got closer it grew taller. I'm pretty sure that means the earth is round.
Well, now this one is just silly.
I'll show you how:
In my city, we have a large valley that is ringed by mountains on three sides, with one small but tallish mountain in the center.
On my side of the valley, I am up a little bit on the side of the mountain, and if I look at the mountain in the center, it appears to be only at eye-level, even though it is only about 6 miles away. Does that mean the mountain is only 5 1/2 feet tall (my height)? No, of course not. If I could instantly teleport myself to the location at the base of the mountain, it would "grow taller" as I got closer, and standing at its base I would suddenly find that the mountain is actually 2,700 feet high!
The phenomenon of the mountain looking shorter on the horizon the further you get away from it is due to perspective - NOT curvature.