  It is demonstrated that iterative repeating of some simple geometric
construction leads unavoidably in the limit to the golden ratio. The procedure
appears to be quickly convergent regardless of a ratio of initial elements
sizes. This could explain a widespread occurrence of the golden ratio in
various constructions, including puzzling proportions encountered in structures
of ancient cultures (e.g., in the Great Pyramid of Giza), as well as in the
natural growth and self-organization processes in organic and inorganic matter.
