Open Access
Translator Disclaimer
2008 Fibonacci sequences and the space of compact sets
Kristina Lund, Steven Schlicker, Patrick Sigmon
Involve 1(2): 197-215 (2008). DOI: 10.2140/involve.2008.1.197

Abstract

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.

Citation

Download Citation

Kristina Lund. Steven Schlicker. Patrick Sigmon. "Fibonacci sequences and the space of compact sets." Involve 1 (2) 197 - 215, 2008. https://doi.org/10.2140/involve.2008.1.197

Information

Received: 19 June 2007; Revised: 22 April 2008; Accepted: 3 May 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1229.52014
MathSciNet: MR2429659
Digital Object Identifier: 10.2140/involve.2008.1.197

Subjects:
Primary: 00A05

Keywords: compact plane sets , Fibonacci , Hausdorff metric , metric geometry

Rights: Copyright © 2008 Mathematical Sciences Publishers

JOURNAL ARTICLE
19 PAGES


SHARE
Vol.1 • No. 2 • 2008
MSP
Back to Top