The Geometry of Projectile's Motion
How to Use the Golden Ratio
How to Determine the Earth's Circumference

How to Determine the Distance to the Horizon

Even before Columbus sailed across the Atlantic Ocean (thus “proving” the Earth was round), mathematicians had already developed a very simple formula to calculate the distance to the horizon. Although many of the people who lived inland in the fifteenth century may have thought that the Earth was flat, no sensible person living on the coast could possibly have held this view. Why? Because people on the coast could see ships gradually drop below the horizon as the ships sailed away.

You can use the following formula to figure out how far the horizon is from you (in miles):

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where height is your height (in feet) plus the height of whatever you happen to be standing on (a ladder, a mountain, anything). If you’re standing on the shore, then you can also estimate the distance to the horizon by simply dividing your height in half. So if you’re 5'6" (5.5 feet) tall, the distance to the horizon is only about 2.75 miles!

The Earth curves faster than most people think. On a small lake — say, 2.5 miles across — there’s a 1-foot-tall bulge in the middle of the lake due to the curvature of the Earth. On some larger bodies of water, if conditions are right, you can actually perceive the curvature of the Earth when this sort of bulge blocks your view of the opposing shore.

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