Fibonacci and Lucas Numbers with Applications

By T. Koshy. 2001

1,978 citations recorded by the source corpus.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/0d10baedc345a631759d217e6b9163c76a1be8ab

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In Geometry and Topology

In Statistical and Nonlinear Physics

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Citations in the corpus

Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory (2005, methodology): “In addition, matrices are widely used in rigid body mechanics [11,344,399,432,449,562], structural dynamics [350,409,467], fluid dynamics [137,200,595], circuit theory [13], queuing and stochastic systems [265,436], graph theory [202], signal processing [569], statistical mechanics [7,69,574], demog”
On The Diophantine equation Fn+Fm=2a (2016, background): “For the beauty and rich applications of these numbers and their relatives one can see Koshy’s book [8].”
On the Number of Summands in Zeckendorf Decompositions (2010, neutral): “5) which, by a well-known identity for binomial sums, equals Fn−1 (for a proof, see either [9] or Appendix A of [8]).”
On the Norms of Toeplitz Matrices Involving Fibonacci and Lucas Numbers (2008, neutral): “The following sum formulae for the Fibonacci and Lucas numbers are well known [3, 7]: (7) n−1 ∑”
A New Generalization of Fibonacci Sequence & Extended Binet's Formula (2009, methodology): “Koshy refers to the Fibonacci numbers as one of the “two shining stars in the vast array of integer sequences,” [18].”
On Complex Fibonacci Quaternions (2013, background): “From [11], it is well known that for the Fibonacci and Lucas numbers Binet formulas are”
Generalized Fibonacci Polynomials and Fibonomial Coefficients (2013, background): “The reader will find an introduction to these well-studied sequences in the books by Koshy [18] and Moll [23].”
Phyllotaxis-inspired nanosieves with multiplexed orbital angular momentum (2021, background): “Statistics showed that 4% of the patterns of pine trees grown in Norway follow the Lucas numbers, while the majority of the rest follow Fibonacci numbers [46].”
On generalized Fibonacci and Lucas polynomials (2009, background): “Introduction In modern science there is a huge interest in the theory and application of the Golden Section and Fibonacci numbers [1–34].”