My dad keeps asking me about a claim I made in my post about the curvature of the Earth: That looking at sea level across a 500 m wide part of a lake, we should be missing the bottom 20 cm of ships moored on the other side. So to shut him up, here are the calculations.

First: This is what we assume:

- The Earth is round.
- Its radius is 6.371 km.
- We can actually see in a straight line and the light isn’t bent by weird things in the air or other processes.

This gives us this situation:

We are situated at position *x* right at water level. We look out tangentially along *b*, so there is a right angle between the radius of the Earth, *a*, and *b*. Side *c* of the triangle we are looking at consists of *c2* (which is equal to *a*, the radius of the Earth) and *c1*, which we are looking for: The height below which we cannot see from position *x*.

We know *a* to be 6,371 km and *b* is 0.5 km. Now we just need to put everything into Pythagoras’ theorem, solve for *c1* and we are done!

Turns out we find *c1* as 19.6 cm. Which is pretty close to the 20 cm I claimed last time, right? Everybody happy now? If you want to look at a more realistic and less simplified calculation – go do it yourself! :-)