Incidence and Symmetry in Design and Architecture

This 1983 text tackles two fundamental mathematical topics: graph theory and the theory of transformation groups.

Jenny A. Baglivo (Author), Jack E. Graver (Author)

9780521297844, Cambridge University Press

Paperback, published 31 March 1983

320 pages
24.5 x 17 x 1.5 cm, 0.45 kg

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.

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.

Subject Areas: Architecture [AM]