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Concepts & Images : Visual Mathematics - A.L. Loeb

Concepts & Images

Visual Mathematics

By: A.L. Loeb

Hardcover Published: 1st November 1992
ISBN: 9780817636203
Number Of Pages: 228

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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 oneĀ­ 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-DimensionĀ­ al), Studio Arts 125b (Design Science Workshop, Three-Dimensional),2 as well as my freshman seminars on Structure in Science and Art.

Preface
Introductionp. 1
Areas and Anglesp. 6
Tessellations and Symmetryp. 14
The Postulate of Closest Approachp. 28
The Coexistence of Rotocentersp. 36
A Diophantine Equation and its Solutionsp. 46
Enantiomorphyp. 57
Symmetry Elements in the Planep. 77
Pentagonal Tessellationsp. 89
Hexagonal Tessellationsp. 101
Dirichlet Domainp. 106
Points and Regionsp. 116
A Look at Infinityp. 122
An Irrational Numberp. 128
The Notation of Calculusp. 137
Integrals and Logarithmsp. 142
Growth Functionsp. 149
Sigmoids and the Seventh-year Trifurcation, a Metaphorp. 159
Dynamic Symmetry and Fibonacci Numbersp. 167
The Golden Trianglep. 179
Quasi Symmetryp. 193
Appendix I: Exercise in Glide Symmetryp. 205
Appendix II: Construction of Logarithmic Spiralp. 207
Bibliographyp. 210
Indexp. 225
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780817636203
ISBN-10: 081763620X
Series: Design Science Collection
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 228
Published: 1st November 1992
Publisher: SPRINGER VERLAG GMBH
Country of Publication: US
Dimensions (cm): 23.39 x 15.6  x 1.42
Weight (kg): 0.52