From Pythagoras to Fourier and From Geometry to Nature

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Editorial

Frontmatter

Pages i-vii

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Editorial

Preface

Pages ix-x

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Editorial

Table of Contents

Pages xi-xiii

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PART I

Book Chapter

Chapter 1. The Pythagorean Theorem and Its Extensions

Pages 3-8

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Chapter 2. Recalling Sequences & Series

Pages 9-10

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Book Chapter

Chapter 3. Hilbert and Metric Spaces

Pages 11-13

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Chapter 4. Fourier and the Trigonometric Series

Pages 15-20

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Chapter 5. Applications

Pages 21-27

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Book Chapter

Chapter 6. Orthogonal Polynomials

Pages 29-38

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Chapter 7. Grandi (Rhodonea) Curves

Pages 39-41

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Book Chapter

Chapter 8. Pseudo-Chebyshev Functions

Pages 43-49

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PART II

Book Chapter

Chapter 9. From Lamé Curves to Gielis Transformations

Pages 53-67

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Chapter 10. Waves and More

Pages 69-77

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Chapter 11. Stretchable Rulers and Integer Shapes

Pages 79-82

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PART III

Book Chapter

Chapter 12. Solution of Problems in Gielis Domains

Pages 85-97

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PART IV

Book Chapter

Chapter 13. From Universal Natural Shapes to Scientific Methodology

Pages 101-114

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Book Chapter

Chapter 14. Understanding Life

Pages 115-127

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Chapter 15. Trigonometry on the Diamond

Pages 129-134

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Reference List

References

Pages 135-146

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