It seems to be the only math which many flat-Earthers are willing to consider accurate. The Earth, they say, supposedly curves away at a rate of eight inches times the distance in miles squared. Which is true. Kind of. But not really.

The figure, which they say comes from NASA, or “science,” actually comes from a very different source. Flat-Earthers, no matter where they got it themselves, owe it to none other than Samuel Birley Rowbotham, author of Zetetic Astronomy. He got it from the Encyclopedia Brittanica, where it is cited under the heading “Leveling.” You’ll find his lengthy quote (I doubt that he got permission to use it, by the way) starting on page 8 of the 1865 edition of his book.

The problem is that this is in the context of civil engineering, not mathematics, and it’s just a rule of thumb employed by plane surveyors to compensate for the drop in a target of the same height as the surveyor’s transit. It builds up inaccuracy as the distance increases for two reasons, the first being that it is not exact, and the second being that it is not based on the formula for a circle. It actually plots out to be a parabola. …

The simple fact is that you can’t answer this question without taking at least two things into account. The first is the height of the observer. I won’t go into the math, because not only is there an excellent online calculator for this, but the math and source code are given for it right here.

The other thing you have to take into account is atmospheric refraction, the fact the different densities of fluids such as air bend light. Flat-Earthers love to invoke refraction to explain sunsets, as much as they like to disparage it as an excuse when viewing distant objects.