Inductive Constructions for Rigidity , 2 day workshop , July 2012
نویسندگان
چکیده
The rigidity and flexibility of a structure, either man-made in buildings, linkages, and lightweight deployable forms, or found in nature ranging from crystals to proteins, is critical to the form, function, and stability of the structure. The mathematical theory of ‘rigidity and flexibility’ is developing methods for the analysis and design of man-made structures, as well as predictions of the behavior of natural structures such as proteins. We live in 3-dimensions, and a fundamental problem is to develop results for 3-dimensions which are as good and as efficient as the recently developed theory for structures in 2-dimensions. One of the key ways to build examples and prove general results is an inductive construction: a sequence of local steps that build all possible structures from a few simple starting examples. Since at least the classic book of Henneberg [7], inductive constructions for infinitesimal rigidity of structures have played a key role in combinatorial characterizations of graphs supporting infinitesimal rigidity and independence of structures [24], [6]. More recently key results in global rigidity of structures were proved using key inductive constructions [1, 4].
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