A ball sliding along a 'Lemniscate' curve takes the same time to arrive at a given point as a ball that takes the direct pathpic.twitter.com/a8FtMonFiE
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I think in this case it is found by solving an Abel-type integral equation. Otherwise, I do not see how the extremum requirement is formulated.
that's a good point .. though of course i used calculus of variations to find the Euler Lagrange equations but that's a cop out lol
