Translations:The principle of least time/6/en

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Pierre de Fermat (1601–1665) formulated the rule known as Fermat’s principle of least time. In his original statement, Fermat asserted that the raypath taken by light traveling between any two points is such that the time taken is a minimum. In other words, the ray-paths are the flow lines. Eventually, Fermat’s original statement underwent some expansion. Fermat’s principle is expressed now as: The raypath taken by light traveling between any two points is such that the time taken is stationary with respect to variations of that path. Stationary means that the traveltime can be a minimum or can be a maximum or can be a point of inflection having a horizontal tangent. More specifically, the traveltime of the true trajectory (i.e., the raypath) will equal, to a first approximation, the traveltime of paths in the immediate vicinity. Energy traveling along these neighboring paths will arrive at the destination at about the same time by routes that differ only slightly. Thus, these neighboring paths will tend to reinforce one another. Energy taking other paths arrives out of phase and therefore tends to cancel out. The net result is that energy effectively propagates along the raypaths (i.e., the paths that satisfy Fermat’s principle). In this way, Fermat’s principle helps explain why light is so clever in its meanderings.