Talk:Great-circle distance

Why is "spherical distance" a better name for this page than great circle distance, which has now been made a redirect page? Is it not standard to speak of "great circle distance"? Michael Hardy 21:26, 5 Oct 2004 (UTC)

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I agree, I think the page has been made, while perhaps mathematically correct, harder to understand by introducing the formulas using spherical coordinates instead of latitude and longitude.

I think it's wise to at least break it up into two sections, one for the math principals behind it, and one for a practical use case (latitude and longitude to find distance).

I always intended for it to be easy to understand. --JeremyCole 17:34, Oct 16, 2004 (UTC)

The article says:

Consider a sphere of radius r centered at the origin. That is, the set of all points (x₁, x₂, x₃) such that

$x_{1}^{2}+x_{2}^{2}+x_{3}^{2}=r^{2}$

The spherical distance between any two points x and y on this sphere is given by

$d(x,y)=r\cos ^{-1}\left({\frac {x_{1}y_{1}+x_{2}y_{2}+x_{3}y_{3}}{r^{2}}}\right).$

Why is this of interest? The spherical distance is r times the angle (in radians). That seems to be the main point. The dot product over r² is the cosine of the angle. Taking the arccosine of the cosine, after using a needlessly complicated expression for the cosine, when one could have said simply "The spherical distance is r times the angle (in radians) would be more to the point. Michael Hardy 23:48, 16 Oct 2004 (UTC)