Abstract

The Fibonacci numbers appear in many surprising situations. We show that Fibonacci-type sequences arise naturally in the geometry of H(R²), the space of all nonempty compact subsets of R² under the Hausdorff metric, as the number of elements at each location between finite sets. The results provide an interesting interplay between number theory, geometry, and topology.

Keywords

Hausdorff metric, Fibonacci, metric geometry, compact plane sets

Mathematical Subject Classification

Primary: 00A05

Authors