Mince pies are gold dust in Chipping Campden.
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The haversine formula1 ‘remains particularly well-conditioned for numerical computation even at small distances’ – unlike calculations based on the spherical law of cosines. The ‘versed sine’ is 1-cosθ, and the ‘half-versed-sine’ (1-cosθ)/2 = sin²(θ/2) as used above. It was published by Roger Sinnott in Sky & Telescope magazine in 1984 (“Virtues of the Haversine”), though known about for much longer by navigators. (For the curious, c is the angular distance in radians, and a is the square of half the chord length between the points). A (surprisingly marginal) performance improvement can be obtained, of course, by factoring out the terms which get squared.
Just as I thought.
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