The Fibonacci track form, with applications in Fibonacci vector geometry

J. C. Turner
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 4, 1998, Number 4, Pages 135–147
Full paper (PDF, 8187 Kb)

Details

Authors and affiliations

J. C. Turner
University of Waikato,
Hamilton, New Zealand

Abstract

A particular form of generalized Fibonacci sequence is defined, and supplied with the generic name track. Reasons for doing this are discussed, and simple examples of tracks are given. Then an example which occurs in Fibonacci Vector Geometry, namely the vector-product track, is treated in some detail.

Keywords

• Generalized Fibonacci sequence
• Fibonacci vector sequence
• Vector-product sequence
• Track
• Track pattern
• Fibonacci words
• Fibonacci vector geometry

AMS Classification

• 11B37
• 11B39
• 10A35

References

1. Wai-Fong Chuan. “Embedding Fibonacci Words into Fibonacci Word Patterns.” In G. Bergum et al. (eds.), Applications of Fibonacci Numbers. 5 Kluwer A. P. 1993: pp 113-127.
2. Wai-Fong Chuan. “Subwords of the Golden Sequence and Fibonacci Words.” In G. Bergum et al. (eds.), Applications of Fibonacci Numbers. 6 Kluwer A. P. 1996: pp 73-84.
3. J. C. Turner. “Fibonacci Word Patterns and Binary Sequences.” The Fibonacci Quar­terly, 26, No. 3, 1988: pp 233-246.
4. J. C. Turner and A. G. Schaake. “On a Model of the Modular Group.” In G. E. Bergum et al. (eds.), Applications of Fibonacci Numbers 6 Kluwer A. P. (1996).
5. J. C. Turner and A. G. Shannon. “Introduction to a Fibonacci Vector Geometry.” In G. E. Bergum et al. (eds.), Applications of Fibonacci Numbers 7 Kluwer A. P. (1998).
6. J. C. Turner. “On Vector Sequence Recurrence Equations in Fibonacci Vector Geom­etry.” In F. Howard et al. (eds.), Applications of Fibonacci Numbers. 8 Kluwer A. P. (1999).
7. J. C. Turner and A.G. Shannon. “On Fibonacci Sequences, Geometry and m-Square Equations.” (to appear, The Fibonacci Quarterly, 1999.)