Geometry of Frameworks

<p><span>This textbook provides a comprehensive and rigorous treatment of the mathematical theory underlying rigidity and the flexibility of frameworks. Integrating classical geometry, modern rigidity theory, and topological methods, the authors develop a unified perspective on how geometric constraints determine the possible motions and configurations of planar and spatial structures.</span></p> <p><span>The book begins by discussing the foundations of rigid motions, infinitesimal rotations, and vector fields, establishing the analytical and algebraic tools required for later chapters. The book then advances to a systematic study of unit-bar frameworks, infinitesimal rigidity, the rigidity matrix, rigidity of graphs and the rigidity and flexibility of a polyhedral surface. Each chapter is accompanied by exercises, with complete solutions provided in the final chapter.</span></p> <p><span>Throughout the book, the authors incorporate historical context, classical theorems, and modern applications in robotics and computational geometry. This book is suitable as a graduate‑level textbook for a course on the geometry of frameworks or as a reference for researchers in geometry, combinatorics, and related applied fields.</span></p>