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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
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Abstract |
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The Fibonacci numbers appear in many surprising situations. We show that Fibonacci-type sequences arise naturally in the geometry of , the space of all nonempty compact subsets of 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
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Mathematical Subject Classification 2000
Primary: 00A05
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Milestones
Received: 19 June 2007
Revised: 22 April 2008
Accepted: 3 May 2008
Published: 1 July 2008
Communicated by Joseph O'Rourke
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Authors |
| Kristina Lund | |
| 5541 Rivertown Circle SW Wyoming, MI 49418 United States |
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| Steven Schlicker | |
| Department of Mathematics 2307 Mackinac Hall Grand Valley State University 1 Campus Drive Allendale, MI 49401-9403 United States |
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| http://faculty.gvsu.edu/schlicks/ | |
| Patrick Sigmon | |
| 11641 Broadfield Court Raleigh, NC 27617 United States |
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