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Shortest Path Between Two Points On A Sphere

submitted by happytoes to mathematics 1.4 yearsOct 12, 2024 14:19:10 ago (+1/-0)     (www.youtube.com)

https://www.youtube.com/watch?v=F1J5CO3Nuf8

Hard core maths content. Instead of assuming that the path is a great circle and working out the distance, the video sets up a formula for integrating the length of an arbitrary path. Then it uses the Euler-Lagrange equation to obtain a differential equation for the shortest path. The resulting nightmare integral needs a clever substitution. Eventually it all simplifies and the path lies in a plane through the center of the sphere.


5 comments block


[ - ] Sector2 0 points 1.4 yearsOct 12, 2024 15:11:53 ago (+0/-0)

The shortest path between two points on a sphere is a direct straight line.

[ - ] happytoes [op] 1 point 1.4 yearsOct 12, 2024 18:26:48 ago (+1/-0)

Are you a mole? You are supposed to stay on the surface!

[ - ] iSnark 0 points 1.4 yearsOct 12, 2024 14:31:50 ago (+0/-0)

There is no such thing as the "shortest path" on a sphere! ALL paths are equidistant!

[ - ] Portmanure 0 points 1.4 yearsOct 12, 2024 15:12:11 ago (+0/-0)

Going through the sphere would be shorter…