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Frank Reed
Thank you for the information on ‘x^2’.  After my post, I kind of worked it out for myself, but by then my post was racing across the ether.

You also wrote: “A "geodesic" is a geometric generalization of the concept of a great circle, ……………………………………  I have not been able to come up with any practical benefit to knowing or even contemplating the long-distance ellipsoidal geodesics.” 

Well, I can think of one example although I'm not sure it passes the 'practical benefit' test: A subject for Master’s Coursework.  We were asked to compare results for the great circle and the geodesic between London and New York.  We were required to calculate the initial course in each direction plus the distances.  It appears that in November 2000, I came close enough to understanding that sort of thing to gain full marks.  Unfortunately, within 30 minutes of submission, it all turned to bagpipe music in my head.  I enclose a photograph of my results by way of comparison between the two methods plus photographs of two out of nine pages of spaghetti numbers to indicate what fun was had producing them.  Appologies for quoting results to one mm and 0.1 of a second and also if I've ever submitted these pages before. DaveP

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