On Visualization of Solutions to Some Extreme Problems

The article discusses the problem of finding a straight line on a plane, the sum of the squares of the distances to which from n given points of this plane will be the smallest. It is shown how to reduce this problem to solving a similar problem for three points, the solution of which is a straight line containing the major axis of the Steiner ellipse of a triangle with vertices at these points. There is also a hypothesis about the connection of the subject under consideration with the problem of the fields of attraction in the theory of fractals.

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