{{Wikipedia}}

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The '''haversine formula''' is an equation important in navigation, giving great-circle distances between two points on a sphere from their longitudes and latitudes.

It is a special case of a more general formula  in spherical trigonometry, the '''law of haversines''', relating the sides and angles of spherical "triangles".


;Task:
Implement a great-circle distance function, or use a library function,
to show the great-circle distance between:
* Nashville International Airport (BNA) &nbsp; in Nashville, TN, USA, &nbsp; which is:
   <big><big> '''N''' 36°7.2',   '''W''' 86°40.2'     (36.12,   -86.67) </big></big>          -and-
* Los Angeles International Airport (LAX) &nbsp;in Los Angeles, CA, USA, &nbsp; which is:
   <big><big> '''N''' 33°56.4',  '''W''' 118°24.0'    (33.94,  -118.40) </big></big>
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<pre>
User Kaimbridge clarified on the Talk page:

 -- 6371.0 km is the authalic radius based on/extracted from surface area;
 -- 6372.8 km is an approximation of the radius of the average circumference
    (i.e., the average great-elliptic or great-circle radius), where the
     boundaries are the meridian (6367.45 km) and the equator (6378.14 km).

Using either of these values results, of course, in differing distances:

 6371.0 km -> 2886.44444283798329974715782394574671655 km;
 6372.8 km -> 2887.25995060711033944886005029688505340 km;
 (results extended for accuracy check:  Given that the radii are only
  approximations anyways, .01' ≈ 1.0621333 km and .001" ≈ .00177 km,
  practical precision required is certainly no greater than about
  .0000001——i.e., .1 mm!)

As distances are segments of great circles/circumferences, it is
recommended that the latter value (r = 6372.8 km) be used (which
most of the given solutions have already adopted, anyways).
</pre>

Most of the examples below adopted Kaimbridge's recommended value of
6372.8 km for the earth radius.  However, the derivation of this
[http://math.wikia.com/wiki/Ellipsoidal_quadratic_mean_radius ellipsoidal quadratic mean radius]
is wrong (the averaging over azimuth is biased).  When applying these
examples in real applications, it is better to use the
[https://en.wikipedia.org/wiki/Earth_radius#Mean_radius mean earth radius],
6371 km.  This value is recommended by the International Union of
Geodesy and Geophysics and it minimizes the RMS relative error between the
great circle and geodesic distance.
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