Ebook: Concepts & Images: Visual Mathematics
Author: Arthur L. Loeb (auth.)
- Tags: Visualization, Mathematical Logic and Foundations, Applications of Mathematics, Computer Imaging Vision Pattern Recognition and Graphics, Signal Image and Speech Processing, Mathematical Methods in Physics
- Series: Design Science Collection
- Year: 1993
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-xi
Introduction....Pages 1-5
Areas and Angles....Pages 6-13
Tessellations and Symmetry....Pages 14-27
The Postulate of Closest Approach....Pages 28-35
The Coexistence of Rotocenters....Pages 36-45
A Diophantine Equation and its Solutions....Pages 46-56
Enantiomorphy....Pages 57-76
Symmetry Elements in the Plane....Pages 77-88
Pentagonal Tessellations....Pages 89-100
Hexagonal Tessellations....Pages 101-105
Dirichlet Domains....Pages 106-115
Points and Regions....Pages 116-121
A Look at Infinity....Pages 122-127
An Irrational Number....Pages 128-136
The Notation of Calculus....Pages 137-141
Integrals and Logarithms....Pages 142-148
Growth Functions....Pages 149-158
Sigmoids and the Seventh-year Trifurcation, a Metaphor....Pages 159-166
Dynamic Symmetry and Fibonacci Numbers....Pages 167-178
The Golden Triangle....Pages 179-192
Back Matter....Pages 205-228
Quasi Symmetry....Pages 193-204
Content:
Front Matter....Pages i-xi
Introduction....Pages 1-5
Areas and Angles....Pages 6-13
Tessellations and Symmetry....Pages 14-27
The Postulate of Closest Approach....Pages 28-35
The Coexistence of Rotocenters....Pages 36-45
A Diophantine Equation and its Solutions....Pages 46-56
Enantiomorphy....Pages 57-76
Symmetry Elements in the Plane....Pages 77-88
Pentagonal Tessellations....Pages 89-100
Hexagonal Tessellations....Pages 101-105
Dirichlet Domains....Pages 106-115
Points and Regions....Pages 116-121
A Look at Infinity....Pages 122-127
An Irrational Number....Pages 128-136
The Notation of Calculus....Pages 137-141
Integrals and Logarithms....Pages 142-148
Growth Functions....Pages 149-158
Sigmoids and the Seventh-year Trifurcation, a Metaphor....Pages 159-166
Dynamic Symmetry and Fibonacci Numbers....Pages 167-178
The Golden Triangle....Pages 179-192
Back Matter....Pages 205-228
Quasi Symmetry....Pages 193-204
....