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Posted By: Andrew PalfreymanThe Lifeguard Problem is interesting. You're standing on the beach and there's someone in trouble in the ocean. What's the fastest route to them, given the speed over sand and the speed in water? The answer turns out to be another way of expressing Snell's Law - refraction.So light chooses the fastest path too.
Posted By: Andrew PalfreymanIndeed. But Fermat's principle is a hypothesis about light minimising its travel time. Snell's Law is a natural consequence of Fermat's principle. My point is that it's a bit peculiar to me that light does indeed take the fastest route. Is there a greater idea at work here?
Posted By: alsetalokinIt seems that you have demonstrated that the perimeters of all three figures are the same.Hence pi=4.
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