ENGLISH

From the Golden Rectangle to the Fibonacci Sequences

By Bat-Sheva Ilany , Opher Liba

Book information

Publisher
Springer
Year
2023
ISBN
9783030975999, 9783030976002
Language
english
Format
PDF
Filesize
10 MB (10584232 bytes)
Series
Springer Texts in Education
Pages
176\176
Time added
2023-07-06 18:52:30

Description

Introduction Contents 1 The Golden Rectangle and the Golden Ratio 1.1  The Golden Rectangle and the Golden Ratio 1.2  Quantitative Attributes of 1.3  The Group of -Numbers 1.4  Matrices and Isomorphism 1.5  The Norm of -Numbers Exercises for Chapter 1 Answers, Hints and Partial Solutions 2 Introducing Golden Triangles 2.1  Wide and Narrow Golden Triangles 2.2  The Angles in Golden Triangles 2.3  Area Ratios 2.4  Pentagons and Pentagrams Exercises for Chapter 2 Answers, Hints and Partial Solutions 3 The Fibonacci Sequence 3.1  The Fibonacci Sequence and the Exponents of the Golden Ratio 3.2  Binet’s Formula 3.3  Key Relationships Between Members of the Sequence 3.4  Sums 3.5  Extending the Sequences 3.6  Matrices and the Fibonacci Sequence Exercises for Chapter 3 Answers, Clues and Partial Solutions 4 The Lucas Sequence 4.1  Three Definitions of the Lucas Sequence 4.2  Connections Between the Fibonacci and Lucas Sequences 4.3  The Powers of the Golden Ratio 4.4  Sums Exercises for Chapter 4 Answers, Hints and Partial Solutions 5 The General Fibonacci-Like Sequences 5.1  Definitions, Binet’s Formulas and Relationships 5.2  Comparing the Fibonacci and the Fibonacci-Like Sequences 5.3  The Lucas-Like Sequence of the Fibonacci-Like Sequence 5.4  Comparing the Fibonacci-Like and Lucas-Like Sequences 5.5  The General Sequence of the Fibonacci-Like Sequence 5.6  The Powers of the Golden Ratio 5.7  Ordering Fibonacci-Like Sequences Exercises for Chapter 5 Answers, Hints and Partial Solutions 6 In Opher’s Footsteps—Challenges for Exploration List of Formulas, Theorems, and Definitions 7 Chapter 1: The Golden Rectangle and the Golden Ratio 7 Chapter 2: Introducing Golden Triangles 7 Chapter 3: The Fibonacci Sequence 7 Chapter 4: The Lucas Sequence 7 Chapter 5: The General Fibonacci-Like Sequences Annotated Bibliography

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