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Look Inside Incidence and Symmetry in Design and Architecture

Incidence and Symmetry in Design and Architecture

$34.99

Part of Cambridge Urban and Architectural Studies

  • Date Published: April 1983
  • availability: Available
  • format: Paperback
  • isbn: 9780521297844

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  • The initial purposes of this 1983 text were to develop mathematical topics relevant to the study of the incidence and symmetry structures of geometrical objects and to expand the reader's geometric intuition. The two fundamental mathematical topics employed in this endeavor are graph theory and the theory of transformation groups. Part I, Incidence, starts with two sections on the basics of graph theory and continues with a variety of specific applications of graph theory. Following this, the text becomes more theoretical; here graph theory is used to study surfaces other than the plane and the sphere. Part II, Symmetry, starts with a section on rigid motions or symmetries of the plane, which is followed by another on the classification of planar patterns. Additionally, an overview of symmetry in three-dimensional space is provided, along with a reconciliation of graph theory and group theory in a study of enumeration problems in geometry.

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    Product details

    • Date Published: April 1983
    • format: Paperback
    • isbn: 9780521297844
    • length: 320 pages
    • dimensions: 244 x 170 x 17 mm
    • weight: 0.51kg
    • availability: Available
  • Table of Contents

    Forward
    Preface
    Part I. Incidence: Introduction
    Section 1. Incidence and Graph Theory:
    1. Topological transformations
    2. Basic graph theory
    3. Directed graphs
    4. Traversability
    5. Distance
    Section II. Incidence in the Plane:
    6. Maps
    7. Planar graphs
    8. Euler's formula
    9. Polyhedra
    Section III. Further Applications of Graph Theory:
    10. Bracing structures
    11. Optimal route design
    12. Mean distance
    13. Triangulations and organization graphs
    Section IV. Topology of Surfaces:
    14. Surfaces
    15. Maps on surfaces
    16. Tesselations of the plane
    17. Compact surfaces
    Part II. Symmetry: Introduction
    Section V. Symmetry and Group Theory:
    18. Planar isometries
    19. Basic group theory
    20. Reflections on the plane
    21. The isometry group of the plane
    Section VI. Symmetry in the Plane:
    22. Discrete groups
    23. The circular groups
    24. The frieze groups
    25. The wallpaper groups
    Section VII. Symmetry in Space:
    26. Space isometries
    27. Discrete space groups
    28. The layer groups
    29. the rod groups
    Section VIII. Symmetry and Enumeration:
    30. A combinational approach to symmetry
    31. Graph symmetry
    32. Enumeration
    33. Fundamental architectural arrangements revisited
    Bibliography
    Indices.

  • Authors

    Jenny A. Baglivo, Fairfield University, Connecticut

    Jack E. Graver, Syracuse University, New York

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