help-gnu-emacs
[Top][All Lists]

## Re: distance from Easter Island to Chile

 From: Emanuel Berg Subject: Re: distance from Easter Island to Chile Date: Mon, 21 Apr 2014 03:50:23 +0200 User-agent: Gnus/5.13 (Gnus v5.13) Emacs/24.3 (gnu/linux)

```Emanuel Berg <address@hidden> writes:

> This is so exact it *could* be used in those "school
> essays" (in which I told not to use the Haversine
> method)

On the Wikipedia article on the Haversine, they mention
the other formula as well - though it is a bit hard to
make sense of... (What is "h"?)

"When using these formulae, ensure that h does not
exceed 1 due to a floating point error (d is only real
for h from 0 to 1). h only approaches 1 for antipodal
points (on opposite sides of the sphere) — in this
region, relatively large numerical errors tend to
arise in the formula when finite precision is
used. Because d is then large (approaching πR, half
the circumference) a small error is often not a major
concern in this unusual case (although there are other
great-circle distance formulas that avoid this
problem). (The formula above is sometimes written in
terms of the arctangent function, but this suffers
from similar numerical problems near h = 1.)

As described below, a similar formula can be written
using cosines (sometimes called the spherical law of
cosines, not to be confused with the law of cosines
for plane geometry) instead of haversines, but if the
two points are close together (e.g. a kilometer apart,
on the Earth) you might end up with cos (d/R) =