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

The Fibonacci numbers appear in many surprising situations. We show that Fibonacci-type sequences arise naturally in the geometry of (2), the space of all nonempty compact subsets of 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.

Hausdorff metric, Fibonacci, metric geometry, compact plane sets
Mathematical Subject Classification 2000
Primary: 00A05
Received: 19 June 2007
Revised: 22 April 2008
Accepted: 3 May 2008
Published: 1 July 2008

Communicated by Joseph O'Rourke
Kristina Lund
5541 Rivertown Circle SW
Wyoming, MI 49418
United States
Steven Schlicker
Department of Mathematics
2307 Mackinac Hall
Grand Valley State University
1 Campus Drive
Allendale, MI 49401-9403
United States
Patrick Sigmon
11641 Broadfield Court
Raleigh, NC 27617
United States