Concepts & Images: Visual Mathematics

ISBN-13: 9781461267164 / Angielski / Miękka / 2012 / 228 str.

Arthur Loeb

Opis

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.

Spis treści

1. Introduction.- 2. Areas and Angles.- 3. Tessellations and Symmetry.- 4. The Postulate of Closest Approach.- 5. The Coexistence of Rotocenters.- 6. A Diophantine Equation and its Solutions.- 7. Enantiomorphy.- 8. Symmetry Elements in the Plane.- 9. Pentagonal Tessellations.- 10. Hexagonal Tessellations.- 11. Dirichlet Domain.- 12. Points and Regions.- 13. A Look at Infinity.- 14. An Irrational Number.- 15. The Notation of Calculus.- 16. Integrals and Logarithms.- 17. Growth Functions.- 18. Sigmoids and the Seventh-year Trifurcation, a Metaphor.- 19. Dynamic Symmetry and Fibonacci Numbers.- 20. The Golden Triangle.- 21. Quasi Symmetry.- Appendix I: Exercise in Glide Symmetry.- Appendix II: Construction of Logarithmic Spiral.