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Concepts & Images

Visual Mathematics

  • Arthur L. Loeb

Part of the Design Science Collection book series (DSC)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Arthur L. Loeb
    Pages 1-5
  3. Arthur L. Loeb
    Pages 6-13
  4. Arthur L. Loeb
    Pages 14-27
  5. Arthur L. Loeb
    Pages 28-35
  6. Arthur L. Loeb
    Pages 36-45
  7. Arthur L. Loeb
    Pages 46-56
  8. Arthur L. Loeb
    Pages 57-76
  9. Arthur L. Loeb
    Pages 77-88
  10. Arthur L. Loeb
    Pages 89-100
  11. Arthur L. Loeb
    Pages 101-105
  12. Arthur L. Loeb
    Pages 106-115
  13. Arthur L. Loeb
    Pages 116-121
  14. Arthur L. Loeb
    Pages 122-127
  15. Arthur L. Loeb
    Pages 128-136
  16. Arthur L. Loeb
    Pages 137-141
  17. Arthur L. Loeb
    Pages 142-148
  18. Arthur L. Loeb
    Pages 149-158
  19. Arthur L. Loeb
    Pages 167-178
  20. Arthur L. Loeb
    Pages 179-192
  21. Arthur L. Loeb
    Pages 193-204
  22. Back Matter
    Pages 205-228

About this book

Introduction

1. Introduction . 1 2. Areas and Angles . . 6 3. Tessellations and Symmetry 14 4. The Postulate of Closest Approach 28 5. The Coexistence of Rotocenters 36 6. A Diophantine Equation and its Solutions 46 7. Enantiomorphy. . . . . . . . 57 8. Symmetry Elements in the Plane 77 9. Pentagonal Tessellations . 89 10. Hexagonal Tessellations 101 11. Dirichlet Domain 106 12. Points and Regions 116 13. A Look at Infinity . 122 14. An Irrational Number 128 15. The Notation of Calculus 137 16. Integrals and Logarithms 142 17. Growth Functions . . . 149 18. Sigmoids and the Seventh-year Trifurcation, a Metaphor 159 19. Dynamic Symmetry and Fibonacci Numbers 167 20. The Golden Triangle 179 21. Quasi Symmetry 193 Appendix I: Exercise in Glide Symmetry . 205 Appendix II: Construction of Logarithmic Spiral . 207 Bibliography . 210 Index . . . . . . . . . . . . . . . . . . . . 225 Concepts and Images is the result of twenty years of teaching at Harvard's Department of Visual and Environmental Studies in the Carpenter Center for the Visual Arts, a department devoted to turning out students articulate in images much as a language department teaches reading and expressing one­ self in words. It is a response to our students' requests for a "handout" and to l our colleagues' inquiries about the courses : Visual and Environmental Studies 175 (Introduction to Design Science), YES 176 (Synergetics, the Structure of Ordered Space), Studio Arts 125a (Design Science Workshop, Two-Dimension­ al), Studio Arts 125b (Design Science Workshop, Three-Dimensional),2 as well as my freshman seminars on Structure in Science and Art.

Keywords

design mathematics synergetics

Authors and affiliations

  • Arthur L. Loeb
    • 1
  1. 1.Department of Visual and Environmental Studies, Carpenter Center for the Visual ArtsHarvard UniversityCambridgeUSA

Bibliographic information