Geometric Folding Algorithms. Linkages, Origami, Polyhedra
This book focuses on geometric folding and unfolding problems, which have been studied in mathematical literature since about 1500. But over the past decade, there has been a surge of interest in these problems due to many applications in natural sciences, computer science, engineering, automobile manufacturing and the arts. The book is divided into three parts and it presents hundreds of results and more than 60 unsolved “open problems” to encourage readers to start their own studies and research. In the first part, the authors deal with one-dimensional (1D) objects (so-called linkages). They describe their history and explain algorithms for their construction, reconfiguration and application. In the second part, they describe 2D objects (so-called papers or origami). They explain their mathematical properties, construction, decomposition and approximation. In the third part, they show 3D objects (called polyhedra) and manipulations with them. Although some of the studied problems are described simply and are easily comprehended, they are nevertheless deep and to understand or to solve them, the reader needs high-school geometry, basic discrete mathematics, linear algebra, differential equations, differential geometry, graph theory, basic calculus, some algorithmic techniques and aspects of complexity theory. The authors explain step-by-step interesting solutions of some folding problems. This splendidly illustrated book can be interesting for advanced undergraduate students in mathematics and computer science as well as for geometers and computer specialists who can find many new ideas and impulses there.