2.5Geometric Analogies Between Trigonometric and Hyperbolic Functions and Basic Identities for Hyperbolic Functions
2.6Millennium Problems in Mathematics and Physics
2.7A New Look at the Binet Formulas
2.8Hyperbolic Fibonacci and Lucas Functions
2.9Recurrent Properties of the Hyperbolic Fibonacci and Lucas Functions
2.10Hyperbolic Properties of the Symmetric Hyperbolic Fibonacci and Lucas Functions
2.11Formulas for Differentiation and Integration
Chapter 3.Applications of the Symmetric Hyperbolic Fibonacci and Lucas Functions
3.1New Geometric Theory of Phyllotaxis (“Bodnar Geometry”)
3.3The Shofar-Like Model of the Universe
Chapter 4.Theory of Fibonacci and Lucas λ-numbers and its Applications
4.1Definition of Fibonacci and Lucas λ-numbers
4.2Representation of the Fibonacci λ-numbers Through Binomial Coefficients
4.3Cassini Formula for the Fibonacci λ-numbers
4.4Metallic Proportions by Vera Spinadel
4.5Representation of the “Metallic Proportions” in Radicals
4.6Representation of the “Metallic Proportions” in the Form of Chain Fraction
4.7Self-similarity Principle and Gazale Formulas
4.8Hyperbolic Fibonacci and Lucas λ-functions
4.9Special Cases of Hyperbolic Fibonacci and Lucas λ-functions
4.10The Most Important Formulas and Identities for the Hyperbolic Fibonacci and Lucas λ-functions
Chapter 5.Hilbert Problems: General Information
5.1A History of the Hilbert Problems
5.3The “Golden” Non-Euclidean Geometry
Chapter 6.Beauty and Aesthetics of Harmony Mathematics
6.1Mathematics: A Loss of Certainty and Authority of Nature
6.2Strategic Mistakes in the Development of Mathematics: The View from the Outside
6.3Beauty and Aesthetics of Harmony Mathematics
6.4Mathematics of Harmony from an Aesthetic Point of View
7.1A Brief History of the Concept of Universe Harmony
7.3Mathematization of Harmony and Harmonization of Mathematics
7.4The Structure of Scientific Revolutions by Thomas Kuhn
7.5Main Conclusions and New Challenges
Preface to the Three-Volume Book
Continuity in the Development of Science
Scientific and technological progress has a long history and passed in its historical development several stages: The Babylonian and Ancient Egyptian culture, the culture of Ancient China and Ancient India, the Ancient Greek culture, the Middle Ages, the Renaissance, the Industrial Revolution of the 18th century, the Great Scientific Discoveries of the 19th century, the Scientific and Technological Revolution of the 20th century and finally the 21st century, which
