FIND THE DISTANCES BETWEEN ANY 5 PLACES USING DISTANCE FORMULA
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FIND THE DISTANCES BETWEEN ANY 5 PLACES USING DISTANCE FORMULA Destance - speed apon time
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To be more general, the distance is not unique. Clearly if you take an arbitrary path from point A to point B you can deform the path and arrive at any distance between some globally minimal distance and maximum if the extrema exist.
One might ask about the shortest path between two points, or all extremal paths. An extremal path is one whose distance is stationary under infinitesimal path variations. Such paths can be not only minima or maxima but also saddle points, if the metric (differential distance function) is not positive definite.
Specifying that one is only interested in extremal paths (a.k.a. geodesics) at least makes the question well posed, but the answer is still not unique. A simple example can be seen on the surface of the globe. Geodesics here are "great circle" paths, arc segments of the largest possible circle on the sphere (e.g. lines of longitude (but not latitude)). If one wants to travel from the North pole to the 0°N 0°W, the shortest path is along the prime meridian through Greenwich. There is one other extremal path which is a maximum, which is traveling to the South pole along the 180° meridian and then North from there along the prime meridian. These two clearly have different distances.
If one wants to get from the North pole to the South pole, there are an infinite number of paths of equal length.
These concepts exist and are more complicated in spaces with metrics which are not positive definite.
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