Concepts & Images: Visual Mathematics
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.
What people are saying - Write a review
We haven't found any reviews in the usual places.
Areas and Angles
Tessellations and Symmetry
The Postulate of Closest Approach
The Coexistence of Rotocenters
A Diophantine Equation and its Solutions
Symmetry Elements in the Plane
An Irrational Number
The Notation of Calculus
Integrals and Logarithms
Sigmoids and the Seventhyear Trifurcation a Metaphor
Dynamic Symmetry and Fibonacci Numbers
The Golden Triangle
Other editions - View all
adjacent meshes angle array asymptotic bisected Buckminster Fuller bugs called Chapter coexistence compounding constant curve curved-edged decimal decrease Design Science diagonals diophantine equation Dirichlet domains distance distinct rotocenters distinct two-fold rotocenters dynamic symmetry edgelength edges enantiomorphically paired equal equation equivalent exponential function Fibonacci numbers finite four-fold rotocenters glide line glide symmetry golden fraction golden gnomon golden ratio golden rectangle golden triangle hence implies independent variable integer intersection interval lattice point length level of resolution lie on mirrors line segments located Loeb logarithmic spiral mirror line motifs mutually congruent Note original parallel parallelogram Pascal's triangle pattern pentagon pentagonal tessellation perpendicular bisector polygon postulate of closest quadrilateral Quasicrystals radians ratio result rotocomplexes shown in Figure sigmoid spiral proper square straight line straight-edged string symmetry configuration symmetry value tessellate the plane tessellation of Figure Theorem three-fold rotocenter tiles translational symmetry two-fold rotational symmetry unit cell unity velocity vertex vertices zero
Symmetry: Cultural-historical and Ontological Aspects of Science-Arts ...
Limited preview - 2007
Foundations for the Future in Mathematics Education
Richard A. Lesh,Eric Hamilton,James J. Kaput
No preview available - 2007