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When action is not least

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Figure

Fig. 1. 共a兲 On a sphere the great circle line ABC starting from the north pole at A is the shortest distance between two points as long as it does not reach the south pole at A ⬘
Fig. 3. Several true harmonic oscillator worldlines with initial event P
Fig. 8. The coffee-cup optical caustic. The caustic shape in panel 共b兲 共a nephroid 兲 was derived by Johann Bernoulli in 1692 共Ref
Fig. 9. An original true worldline, labeled 0, starts at initial event P. We draw an arbitrary adjacent curve, labeled 1, anchored at two ends on P and a later event R on the original worldline
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