Vol. 1, No. 2, 2008

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Fibonacci sequences and the space of compact sets

Kristina Lund, Steven Schlicker and Patrick Sigmon

Vol. 1 (2008), No. 2, 197–215
Abstract

The Fibonacci numbers appear in many surprising situations. We show that Fibonacci-type sequences arise naturally in the geometry of $\mathsc{ℋ}\left({ℝ}^{2}\right)$, the space of all nonempty compact subsets of ${ℝ}^{2}$ 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
Primary: 00A05