ATRACTOR

Note, in the app below, that when the side of the regular heptagon coincides with the side of the regular polygon with \(14\) sides, the longest diagonal of the latter polygon is twice the longest diagonal of the regular heptagon. And, therefore, the ratio between the longest diagonal and the side of a regular polygon with \(14\) sides is twice the ratio between the longest diagonal and the side of a regular polygon with \(7\) sides.

Instructions: move the red dot to one of the vertices of the regular polygon with \(14\) sides.