|
" Concepts & Images "
by Arthur L. Loeb.
| Document Type
|
:
|
BL
|
| Record Number
|
:
|
573451
|
| Doc. No
|
:
|
b402670
|
| Main Entry
|
:
|
Loeb, Arthur L.
|
| Title & Author
|
:
|
Concepts Images : Visual Mathematics /\ by Arthur L. Loeb.
|
| Publication Statement
|
:
|
Boston, MA :: Birkhäuser Boston :: Imprint: Birkhäuser,, 1993.
|
| Series Statement
|
:
|
Design Science Collection, A Pro Scientia Viva Title
|
| ISBN
|
:
|
9781461203438
|
|
|
:
|
: 9781461267164
|
| Contents
|
:
|
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.
|
| Abstract
|
:
|
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.
|
| Subject
|
:
|
Mathematics.
|
| Subject
|
:
|
Computer vision.
|
| Subject
|
:
|
Visualization.
|
| Subject
|
:
|
Logic, Symbolic and mathematical.
|
| Subject
|
:
|
Mathematical physics.
|
| Added Entry
|
:
|
SpringerLink (Online service)
|
| |