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A more practical way to solve the problem: model it.

Get a few nails, a piece of string, and a thin dowel. The dowel represents represents the riverbank. Afix the dowel to your wall. Hammer two nails in at appropriate distances to represent the barn and house. Run the string from the hours nail over the dowel to the barn nail. Apply a little oil to the dowel so that the string slides easily. Pull the string taut. You're done. This, of course, is a simple modification of the method for finding a great circle on the globe. In both cases, we're looking for a path of least distance, and if you stretch a slightly elastic string (or better yet, a rubber band) over the surface of a globe or in a model of the house-river-barn scenario, it will automatically settle to a lowest energy state which, for elastic materials, is the shortest distance. And once again, this is a simple way to solve optical problems, too.

Frank Reed