Applications of Fibonacci Numbers

Multidimensional Golden Means.- A Necessary and Sufficient Condition that Rays of A Star Configuration on Pascal's Triangle Cover Its Center With Respect to GCD and LCM.- On the Minimal Center Covering Stars With Respect to GCD In Pascal's Pyramid and Its Generalizations.- An Extension of an Old Classical Diophantine Problem.- Fourier Analysis in Finite Nilpotent Groups.- Wall and Vinson Revisited.- Designer Decimals: Fractions Which Contain Second Order Recursion Sequences in Their Decimal Expansions, Reading Left to Right or Right to Left.- Semigroup Presentations and Number Sequences.- Counting the Number of Solutions of Congruences.- On the Number of Overlapping Success Runs in A Sequence of Independent Bernoulli Trials.- Embedding Fibonacci Words Into Fibonacci Word Patterns.- On Sums of Cubes of Fibonacci Numbers.- Integer Sided Triangles Whose Ratio of Altitude to Base Is an Integer.- On a class of Iterative Recurrence Relations.- Discrete Operational Calculi for Two-Sided Sequences.- Transformations of Fibonacci-Lucas Identities.- Fibonacci Numbers and Continued Fraction Expansions.- The DFF and DFFZ Triangles and Their Mathematical Properties.- Contributions from Cascaded Combinations to the Naming of Special Permutations.- The Zeckendorf Representation of {Fkn/Fn}.- Fractal Patterns Derived from Rational Binomial Coefficients.- Hausdorff Dimension in Pascal's Triangle.- Chaos, Elliptic Curves and All that.- Co-Related Sequences Satisfying the General Second Order Recurrence Relation.- On the Moments of The Sum-of-Digits Function.- Problems on Fibonacci and B-Adic Tree Representations by Regular K-Gons.- Two-Distance Sets and the Golden Ratio.- A Fibionacci Problem Classification Scheme Useful to Undergraduate Pedagogy.- Zeckendorf Representations of Positive and Negative Integers by Pell Numbers.- Integration Sequences of Fibonacci and Lucas Polynomials.- Pell-Type Number Generators of Pythagorean Triples.- Balance Morphology of a Binary Tree.-