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It is certainly intuitively clear that the geodesics on the sphere are the great circles. But, showing that seems to be a bit tricky...

I tried working out the Christoffel symbols, and then plugging that into the differential equations for the geodesics, and aside from it being a bit of a mess, I'm up against a bit of a wall with the system.

Now, perhaps I just need to grind it a little more, and it will all fall out, but, I can't help but wonder if there is a better way to "show" what the geodesics of a surface are.

I've had the same issue with the cylinder...

Any tips, to just point me in the right direction, I'd be most appreciative.

Thanks,

-FC

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# The Great Circle et al

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