Preface:

Origami is an ancient art that allows us to fold flat sheets of paper into complex, three-dimensional structures. In the last few decades, we have developed the mathematics to design and analyze new fold patterns, transforming origami from a form of recreation into a powerful engineering tool. This seminar discussed the principles behind origami-inspired design, focusing on geometry and spatial reasoning. It addressed both mathematical theory and applications, covering questions such as: How can we predict from the crease lines and angles on a fold pattern what the resulting 3-D shape will be? How do we do the reverse process of flattening a 3-D shape into a fold pattern? How do we think about action origami (fold patterns that can still move after folding)? And how can these structures and modeling techniques be used in areas such as robotics, manufacturing, space exploration, and medicine? Along the way, we developed an understanding of the engineering method (similar to the scientific method), and of the history of origami as an art form. Seminar participants taught in a broad range of fields, including the arts, history and social studies as well as science and mathematics.