Klappentext

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

Zusammenfassung
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.

Inhalt

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.