The Fermat–Weber point for a set of points ... in the plane is the point ... that minimizes the sum of the Euclidean distances from ... to the points of ... . A ... -chain of a regular ... -gon, denoted by ... , is the segment of the boundary of the regular ... -gon formed by a set of ... consecutive vertices of the regular ... -gon. Here we consider chains with an odd number of vertices whose middle vertex is ... . This Demonstration shows that for every fixed odd positive integer ... , as ... increases, the (blue) Fermat–Weber point of ... moves on the ... axis toward the point ... on the boundary of the chain. It is also shown that when ... exceeds a certain integer, say ... , the (red) Fermat–Weber point of ... coincides with the vertex of the chain ... lying on the ... axis.


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