Maps traditionally aim to preserve lengths and angles (isometries) up to an overall scale factor, often through smooth deformations. Artists are not bound by these constraints, and have long employed sharp folds (in origami) and discontinuous cuts (in kirigami) to transform a simple sheet of paper into complex shapes, e.g. dragons! I will describe how science and mathematics are slowly beginning to catch up with these remarkably imaginative empirical ways, and discuss theorems, algorithms and protocols for the design and control of shape across scales, from the atomic to the architectural. Using demonstrations, I will discuss 2D kirigami tilings for planar shape design, 3D origami tessellations for emulating complex surfaces, and innovative 4D printing and growth strategies for creating dynamic models of flowers and faces. I will conclude with a discussion of some open problems in the field, inviting collaboration and further exploration.
| Organization/Institution | Position | Period |
|---|---|---|
| Lola England de Valpine Professor of Applied Mathematics, of Organismic and Evolutionary
Biology, and of Physics, Harvard University |
Professor | 2003-present |