CAREER: Fundamental Research in Geometric Folding

Massachusetts Institute Of Technology, Cambridge MA

Investigators

Abstract

ABSTRACT PROPOSAL: 0347776 INSTITUTION: MIT PRINCIPAL INVESTIGATOR: Demaine, Erik D. TITLE: CAREER: Fundamental Research in Geometric Folding CAREER: Fundamental Research in Geometric Folding Folding and unfolding is an emerging field of computational geometry studying the continuous motion and reconfiguration of geometric objects such as linkages, paper, and polyhedra and their physical manifestations such as proteins, packaging, and sheet metal. Folding problems arise in surprisingly many contexts, ranging from pure computational geometry to ad-hoc wireless networks to protein folding. This research aims to build a basic theory of geometric folding and, as this theory develops, to explore potential applications throughout science and engineering. Potential applications include air-bag design, space deployment, and drug design. This research addresses several fundamental unsolved problems in geometric folding. How can one efficiently compute motions that reconfigure a planar chain linkage between any two desired configurations? Do such motions always exist for 3D chain linkages whose edge lengths are all equal? Which configurations of proteins (viewed as a 3D chain linkage) can be biosynthesized by a ribosome? How efficiently can one-design proteins in the hydrophobic-hydrophilic model that fold stably into a desired shape? How efficiently can wireless beacons locate themselves in a global geometry given just local information about their neighbors? How efficiently can be design optimal foldings of paper into desired shapes? How many pieces must a polyhedron be cut into to unfold without overlap? In addition to solving problems such as these, the investigator is coauthoring a book about folding and is pursuing education of folding both as an interesting area in its own right and as a vehicle for presenting material in other areas.