Incidence and Symmetry in Design and Architecture

This insightful text explores graph theory and transformation groups, enhancing geometric understanding and intuition in design and architecture through incidence and symmetry.

The 1983 text Incidence and Symmetry in Design and Architecture aims to enhance the understanding of geometric structures through mathematical concepts. It focuses on two primary areas: graph theory and the theory of transformation groups, which serve as foundational tools for exploring incidence and symmetry in geometrical objects. The objective is to cultivate the reader's geometric intuition while providing a robust mathematical framework.

Part I, titled Incidence, begins with an introduction to the basics of graph theory. It then delves into various applications of these concepts, demonstrating how they can be utilized to analyze surfaces beyond the traditional plane and sphere. This section transitions from practical applications to more theoretical explorations, allowing readers to appreciate the depth and versatility of graph theory in geometrical studies.

The second part, Symmetry, introduces the principles of rigid motions and planar symmetries. It includes a classification of patterns found in the plane and extends the discussion to three-dimensional symmetry. Furthermore, this section reconciles graph theory with group theory, providing insights into enumeration problems in geometry. Through Incidence and Symmetry in Design and Architecture, readers gain a comprehensive understanding of how these mathematical theories intersect with design and architecture, enhancing their appreciation of geometric beauty and complexity.