#### 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