



 
Hi Will, Let me try with some diagrams. In the diagram below you are at the green dot on the surface of the Earth and the horizontal line is your line of sight. The horizontal scale is in miles. The vertical scale is in inches and the red dot below the 1 mile indicator is 8 inches below the line of sight. The red dot below the 2 mile indicator is 16 inches below the line of sight. The remaining red dots are 24, 32 and 40 inches below the line of sight respectively. If you look carefully you will see that the red dots lie on a straight line. The problem with your reasoning is that, because of the curvature of the surface of the Earth, the surface of the Earth drops away from the line of sight more quickly than linearly. I hope this helps,  


Math Central is supported by the University of Regina and the Imperial Oil Foundation. 