A straight line may be the shortest 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 between two points, but a "Brachistochrone" curve is the path of least timepic.twitter.com/aWPoz9X6i9
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Which means that you should have a speed of 0.8958 times the speed of the light to see the showed ellipse as a circle.pic.twitter.com/H1qcuOAYQe
i think you'd need to integrate the length contraction along the path since the velocity is changing due to acceleration
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I was just considering a constant speed for illustration.
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but then it wouldn't be a tautochrone or a bachristochrone
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