Revisiting Fibonacci Numbers Through a Computational Experiment - Info and Reading Options

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Intro -- Revisiting Fibonacci Numbers through a Computational Experiment -- Revisiting Fibonacci Numbers through a Computational Experiment -- Contents -- Preface -- Acknowledgments -- Chapter 1 -- Theoretical Background: Fibonacci Numbers as a Framework for Information vs. Explanation Cognitive Paradigm -- 1.1. Introduction -- 1.2. Goals of the Book -- 1.3. A Pedagogy of the Book -- 1.4. Collateral Learning and Hidden Mathematics Curriculum -- 1.5. TITE Problems as a Framework for the Information vs. Explanation Paradigm -- 1.6. Summary -- Chapter 2 -- From Fibonacci Numbers to Fibonacci-Like Polynomials -- 2.1. The Binary Number System and Fibonacci Numbers -- 2.2. Different Representations of Fibonacci Numbers -- 2.3. Fibonacci Numbers and Pascal's Triangle -- 2.4. Hidden Mathematics Curriculum of Pascal's Triangle -- 2.5. Binomial Coefficients and Fibonacci Numbers -- 2.6. From Pascal's Triangle to Fibonacci-Like Polynomials -- 2.7. Other Classes of Polynomials Associated with Fibonacci Numbers -- 2.8. Summary -- Chapter 3 -- Different Approaches to the Development of Binet's Formulas -- 3.1. Fibonacci-Like Numbers -- 3.2. Parameterization of Fibonacci Recursion -- 3.3. Deriving Binet's Formulas for Recurrence (3.8) Using The Machinery of Matrices -- 3.4. Generating Function Approach to the Derivation of Binet's Formulas -- 3.4.1. The Case of Fibonacci Numbers -- 3.4.2. The Case of Lucas Numbers -- 3.4.3. The Case of Matijasevic Numbers -- 3.4.4. The Case of Jacobsthal Numbers -- 3.5. Characteristic Equation Approach -- 3.5.1. The Case of Fibonacci Numbers -- 3.5.2. The Case of Lucas Numbers -- 3.5.3. The Case of Matijasevic Numbers -- 3.5.4. The Case of Jacobsthal Numbers -- 3.6. Continued Fractions and the Golden Ratio -- 3.7. Leibniz Diagrams as Level Lines for Eigenvalues

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